diff --git a/.obsidian/appearance.json b/.obsidian/appearance.json index 961372ea..5a092cc3 100644 --- a/.obsidian/appearance.json +++ b/.obsidian/appearance.json @@ -8,7 +8,6 @@ "hide_excalibrain_ui", "tabs_on_multiple_rown", "popup_preview_size", - "checkboxes", "darkmode", "breadcrumbs", "[ui] Ultra Compact Tab Header", @@ -29,19 +28,20 @@ "omts-MySnippets", "omts-Day Planner (Ivan Lednev)", "omts-[ui] Compact Sidebar", - "omts-[editor] Compact Right Sidebar notes", "latex_mathjax", "day_planner", "dataview", "omts-[ui] Compact Tab Header", - "general_interface", "compact_tabs", "ITS-checkboxes", "supercharged-links-gen", "stacked_tabs", "vertical_stacked_tabs", "headers", - "custom_callouts" + "custom_callouts", + "general_interface", + "omts-[editor] Compact Right Sidebar notes", + "checkboxes" ], "interfaceFontFamily": "CMU Bright,CMU Sans Serif,FiraCode Nerd Font", "textFontFamily": "CMU Sans Serif,FiraCode Nerd Font,CMU Serif", diff --git a/.obsidian/snippets/omts-[editor] Compact Right Sidebar notes.css b/.obsidian/snippets/omts-[editor] Compact Right Sidebar notes.css index 4c559ab7..d9304fb7 100644 --- a/.obsidian/snippets/omts-[editor] Compact Right Sidebar notes.css +++ b/.obsidian/snippets/omts-[editor] Compact Right Sidebar notes.css @@ -47,510 +47,510 @@ } } -/* Duotone hover */ - -/* Light themes */ -.theme-light.minimal-default-light .mod-top-right-space .markdown-reading-view:not(:hover) { - filter: url('data:image/svg+xml,\ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - #filter'); -} - -.theme-light.minimal-atom-light .mod-top-right-space .markdown-reading-view:not(:hover) { - filter: url('data:image/svg+xml,\ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - #filter'); -} - -.theme-light.minimal-ayu-light .mod-top-right-space .markdown-reading-view:not(:hover) { - filter: url('data:image/svg+xml,\ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - #filter'); -} - -.theme-light.minimal-catppuccin-light .mod-top-right-space .markdown-reading-view:not(:hover) { - filter: url('data:image/svg+xml,\ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - #filter'); -} - -.theme-light.minimal-everforest-light .mod-top-right-space .markdown-reading-view:not(:hover) { - filter: url('data:image/svg+xml,\ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - #filter'); -} - -.theme-light.minimal-gruvbox-light .mod-top-right-space .markdown-reading-view:not(:hover) { - filter: url('data:image/svg+xml,\ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - #filter'); -} - -.theme-light.minimal-macos-light .mod-top-right-space .markdown-reading-view:not(:hover) { - filter: url('data:image/svg+xml,\ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - #filter'); -} - -.theme-light.minimal-nord-light .mod-top-right-space .markdown-reading-view:not(:hover) { - filter: url('data:image/svg+xml,\ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - #filter'); -} - -.theme-light.minimal-notion-light .mod-top-right-space .markdown-reading-view:not(:hover) { - filter: url('data:image/svg+xml,\ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - #filter'); -} - -.theme-light.minimal-rose-pine-light .mod-top-right-space .markdown-reading-view:not(:hover) { - filter: url('data:image/svg+xml,\ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - #filter'); -} - -.theme-light.minimal-solarized-light .mod-top-right-space .markdown-reading-view:not(:hover) { - filter: url('data:image/svg+xml,\ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - #filter'); -} - -.theme-light.minimal-things-light .mod-top-right-space .markdown-reading-view:not(:hover) { - filter: url('data:image/svg+xml,\ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - #filter'); -} - - -/* Dark themes */ - -.theme-dark.minimal-default-dark .mod-top-right-space .markdown-reading-view:not(:hover) { - filter: url('data:image/svg+xml,\ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - #filter'); -} - -.theme-dark.minimal-atom-dark .mod-top-right-space .markdown-reading-view:not(:hover) { - filter: url('data:image/svg+xml,\ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - #filter'); -} - -.theme-dark.minimal-ayu-dark .mod-top-right-space .markdown-reading-view:not(:hover) { - filter: url('data:image/svg+xml,\ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - #filter'); -} - -.theme-dark.minimal-catppuccin-dark .mod-top-right-space .markdown-reading-view:not(:hover) { - filter: url('data:image/svg+xml,\ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - #filter'); - /* removed .2 from light values text overlay legibility */ -} - -.theme-dark.minimal-dracula-dark .mod-top-right-space .markdown-reading-view:not(:hover) { - filter: url('data:image/svg+xml,\ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - #filter'); -} - -.theme-dark.minimal-everforest-dark .mod-top-right-space .markdown-reading-view:not(:hover) { - filter: url('data:image/svg+xml,\ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - #filter'); -} - -.theme-dark.minimal-gruvbox-dark .mod-top-right-space .markdown-reading-view:not(:hover) { - filter: url('data:image/svg+xml,\ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - #filter'); -} - -.theme-dark.minimal-macos-dark .mod-top-right-space .markdown-reading-view:not(:hover) { - filter: url('data:image/svg+xml,\ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - #filter'); -} - -.theme-dark.minimal-nord-dark .mod-top-right-space .markdown-reading-view:not(:hover) { - filter: url('data:image/svg+xml,\ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - #filter'); -} - -.theme-dark.minimal-notion-dark .mod-top-right-space .markdown-reading-view:not(:hover) { - filter: url('data:image/svg+xml,\ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - #filter'); -} - -.theme-dark.minimal-rose-pine-dark .mod-top-right-space .markdown-reading-view:not(:hover) { - filter: url('data:image/svg+xml,\ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - #filter'); -} - -.theme-dark.minimal-solarized-dark .mod-top-right-space .markdown-reading-view:not(:hover) { - filter: url('data:image/svg+xml,\ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - #filter'); -} - -.theme-dark.minimal-things-dark .mod-top-right-space .markdown-reading-view:not(:hover) { - filter: url('data:image/svg+xml,\ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - \ - #filter'); -} +/* /* Duotone hover */ */ +/**/ +/* /* Light themes */ */ +/* .theme-light.minimal-default-light .mod-top-right-space .markdown-reading-view:not(:hover) { */ +/* filter: url('data:image/svg+xml,\ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* #filter'); */ +/* } */ +/**/ +/* .theme-light.minimal-atom-light .mod-top-right-space .markdown-reading-view:not(:hover) { */ +/* filter: url('data:image/svg+xml,\ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* #filter'); */ +/* } */ +/**/ +/* .theme-light.minimal-ayu-light .mod-top-right-space .markdown-reading-view:not(:hover) { */ +/* filter: url('data:image/svg+xml,\ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* #filter'); */ +/* } */ +/**/ +/* .theme-light.minimal-catppuccin-light .mod-top-right-space .markdown-reading-view:not(:hover) { */ +/* filter: url('data:image/svg+xml,\ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* #filter'); */ +/* } */ +/**/ +/* .theme-light.minimal-everforest-light .mod-top-right-space .markdown-reading-view:not(:hover) { */ +/* filter: url('data:image/svg+xml,\ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* #filter'); */ +/* } */ +/**/ +/* .theme-light.minimal-gruvbox-light .mod-top-right-space .markdown-reading-view:not(:hover) { */ +/* filter: url('data:image/svg+xml,\ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* #filter'); */ +/* } */ +/**/ +/* .theme-light.minimal-macos-light .mod-top-right-space .markdown-reading-view:not(:hover) { */ +/* filter: url('data:image/svg+xml,\ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* #filter'); */ +/* } */ +/**/ +/* .theme-light.minimal-nord-light .mod-top-right-space .markdown-reading-view:not(:hover) { */ +/* filter: url('data:image/svg+xml,\ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* #filter'); */ +/* } */ +/**/ +/* .theme-light.minimal-notion-light .mod-top-right-space .markdown-reading-view:not(:hover) { */ +/* filter: url('data:image/svg+xml,\ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* #filter'); */ +/* } */ +/**/ +/* .theme-light.minimal-rose-pine-light .mod-top-right-space .markdown-reading-view:not(:hover) { */ +/* filter: url('data:image/svg+xml,\ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* #filter'); */ +/* } */ +/**/ +/* .theme-light.minimal-solarized-light .mod-top-right-space .markdown-reading-view:not(:hover) { */ +/* filter: url('data:image/svg+xml,\ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* #filter'); */ +/* } */ +/**/ +/* .theme-light.minimal-things-light .mod-top-right-space .markdown-reading-view:not(:hover) { */ +/* filter: url('data:image/svg+xml,\ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* #filter'); */ +/* } */ +/**/ +/**/ +/* /* Dark themes */ */ +/**/ +/* .theme-dark.minimal-default-dark .mod-top-right-space .markdown-reading-view:not(:hover) { */ +/* filter: url('data:image/svg+xml,\ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* #filter'); */ +/* } */ +/**/ +/* .theme-dark.minimal-atom-dark .mod-top-right-space .markdown-reading-view:not(:hover) { */ +/* filter: url('data:image/svg+xml,\ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* #filter'); */ +/* } */ +/**/ +/* .theme-dark.minimal-ayu-dark .mod-top-right-space .markdown-reading-view:not(:hover) { */ +/* filter: url('data:image/svg+xml,\ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* #filter'); */ +/* } */ +/**/ +/* .theme-dark.minimal-catppuccin-dark .mod-top-right-space .markdown-reading-view:not(:hover) { */ +/* filter: url('data:image/svg+xml,\ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* #filter'); */ +/* /* removed .2 from light values text overlay legibility */ */ +/* } */ +/**/ +/* .theme-dark.minimal-dracula-dark .mod-top-right-space .markdown-reading-view:not(:hover) { */ +/* filter: url('data:image/svg+xml,\ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* #filter'); */ +/* } */ +/**/ +/* .theme-dark.minimal-everforest-dark .mod-top-right-space .markdown-reading-view:not(:hover) { */ +/* filter: url('data:image/svg+xml,\ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* #filter'); */ +/* } */ +/**/ +/* .theme-dark.minimal-gruvbox-dark .mod-top-right-space .markdown-reading-view:not(:hover) { */ +/* filter: url('data:image/svg+xml,\ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* #filter'); */ +/* } */ +/**/ +/* .theme-dark.minimal-macos-dark .mod-top-right-space .markdown-reading-view:not(:hover) { */ +/* filter: url('data:image/svg+xml,\ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* #filter'); */ +/* } */ +/**/ +/* .theme-dark.minimal-nord-dark .mod-top-right-space .markdown-reading-view:not(:hover) { */ +/* filter: url('data:image/svg+xml,\ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* #filter'); */ +/* } */ +/**/ +/* .theme-dark.minimal-notion-dark .mod-top-right-space .markdown-reading-view:not(:hover) { */ +/* filter: url('data:image/svg+xml,\ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* #filter'); */ +/* } */ +/**/ +/* .theme-dark.minimal-rose-pine-dark .mod-top-right-space .markdown-reading-view:not(:hover) { */ +/* filter: url('data:image/svg+xml,\ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* #filter'); */ +/* } */ +/**/ +/* .theme-dark.minimal-solarized-dark .mod-top-right-space .markdown-reading-view:not(:hover) { */ +/* filter: url('data:image/svg+xml,\ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* #filter'); */ +/* } */ +/**/ +/* .theme-dark.minimal-things-dark .mod-top-right-space .markdown-reading-view:not(:hover) { */ +/* filter: url('data:image/svg+xml,\ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* \ */ +/* #filter'); */ +/* } */ diff --git a/S2 LOGOS . mathématiques pour non spécialistes.md b/S2 LOGOS . mathématiques pour non spécialistes.md index 48c1a864..06fd4904 100644 --- a/S2 LOGOS . mathématiques pour non spécialistes.md +++ b/S2 LOGOS . mathématiques pour non spécialistes.md @@ -30,5 +30,7 @@ share_updated: 2026-01-12T23:01:48+01:00 - [[boule ouverte]] - [[espace métrique]] - [[espace topologique]], [[structure de topologie|topologie]] + - [[topologie engendrée]], [[topologie discrète]], [[topologie grossière]] + - définition des [[partie fermée d'un espace métrique|fermés]] comme complémentaires des ouverts dans un espace topologique diff --git a/organisation physique.md b/organisation physique.md index 7a8980c3..31823aab 100644 --- a/organisation physique.md +++ b/organisation physique.md @@ -1,7 +1,8 @@ -up::[[réseau informatique]] -title::"types d'architectures de réseau" -#s/informatique - ----- +--- +up: "[[réseau informatique]]" +title: "types d'architectures de réseau" +tags: + - "#s/informatique" +--- ![[Réseau informatique architectures.svg]] \ No newline at end of file diff --git a/projet M.chanson.md b/projet M.chanson.md index 08e61f48..e1d91f4f 100644 --- a/projet M.chanson.md +++ b/projet M.chanson.md @@ -1,5 +1,5 @@ --- -difficulty: 0 +difficulty: 5 due: 2024-04-01 up: "[[devoirs]]" tags: diff --git a/python module collections.md b/python module collections.md index 34a6cd14..6cb63386 100644 --- a/python module collections.md +++ b/python module collections.md @@ -1,26 +1,25 @@ --- -description: | - - [[python collections namedtuples|namedtuples]] - - [[python collections deque|deque]] - - [[python collections ChainMap|ChainMap]] - - [[python collections Counter|Counter]] - - [[python collections OrderedDict|OrderedDict]] - - [[python collections defaultdict|defaultdict]] - - [[python collections UserDict|UserDict]] - - [[python collections UserList|UserList]] - - [[python collections UserString|UserString]] +down: + - "[[python collections namedtuples|namedtuples]]" + - "[[python collections deque|deque]]" + - "[[python collections ChainMap|ChainMap]]" + - "[[python collections Counter|Counter]]" + - "[[python collections OrderedDict|OrderedDict]]" + - "[[python collections defaultdict|defaultdict]]" + - "[[python collections UserDict|UserDict]]" + - "[[python collections UserList|UserList]]" + - "[[python collections UserString|UserString]]" +up: "[[python modules]]" +title: "des types conteneurs alternatifs" +tags: + - "#s/informatique/langage/python" --- -up::[[python modules]] -title::"des types conteneurs alternatifs" -#s/informatique/langage/python ----- - -> [!query] Sous-notes de `=this.file.link` -> ```dataview -> LIST title -> FROM -#cours AND -#exercice AND -"daily" AND -#excalidraw AND -#MOC -> WHERE any(map([up, up.up, up.up.up, up.up.up.up], (x) => econtains(x, this.file.link))) -> WHERE file != this.file -> SORT up!=this.file.link, up.up.up.up, up.up.up, up.up, up, file.name -> ``` +```breadcrumbs +title: "Sous-notes" +type: tree +collapse: false +show-attributes: [field] +field-groups: [downs] +depth: [0, 0] +``` diff --git a/python modules.md b/python modules.md index 0b39d13a..e2467379 100644 --- a/python modules.md +++ b/python modules.md @@ -1,8 +1,9 @@ -up::[[python]] -title::"liste de modules python" -#s/informatique/langage/python +--- +up: "[[python]]" +tags: + - "#s/informatique/langage/python" +--- ----- > [!query] sous-notes directes de `=this.file.link` > ```dataview diff --git a/sources/Adám Brudzewsky.md b/sources/Adám Brudzewsky.md index 2465cb12..52eff84c 100644 --- a/sources/Adám Brudzewsky.md +++ b/sources/Adám Brudzewsky.md @@ -1,9 +1,15 @@ -#t/personne +--- +link: "" +tags: + - "#t/personne" +--- - -```dataview -LIST title -FROM "" -WHERE contains(author, this.file.link) +[[APL]] +```breadcrumbs +title: "Sous-notes" +type: tree +collapse: false +show-attributes: [field] +field-groups: [downs] +depth: [0, 0] ``` - diff --git a/structure de topologie.md b/structure de topologie.md index e5d5e644..5035ccc6 100644 --- a/structure de topologie.md +++ b/structure de topologie.md @@ -15,10 +15,21 @@ tags: > - $\mathcal{O}$ est stable par intersection **finie** ^definition +```breadcrumbs +title: "Sous-notes" +type: tree +collapse: false +show-attributes: [field] +field-groups: [downs] +depth: [0, 0] +``` # Propriétés # Exemples + - [[topologie grossière]] + - [[topologie discrète]] + - topologie de Zariski - topologie sur les fonctions $\mathscr{C}^{\infty}$ à [[support d'une fonction|support]] [[espace métrique compact|compact]] diff --git a/tangente hyperbolique d'une somme.md b/tangente hyperbolique d'une somme.md index 94e3e232..296855dc 100644 --- a/tangente hyperbolique d'une somme.md +++ b/tangente hyperbolique d'une somme.md @@ -1,13 +1,15 @@ --- alias: "th(a+b)" +up: "[[formules de trigonométrie]]" +sibling: "[[tangente d'une somme]]" +type: + - "formule de somme" + - "hyperbolique" +tags: + - "#s/maths/trigonométrie" --- -up::[[formules de trigonométrie]] -sibling::[[tangente d'une somme]] -type::"formule de somme", "hyperbolique" title::"$\mathrm{th}(a+b) = \dfrac{\mathrm{th}(a)+\mathrm{th}(b)}{1-\mathrm{th}(a)\mathrm{th}(b)}$" -#s/maths/trigonométrie ----- $\mathrm{th}(a+b) = \dfrac{\mathrm{th}(a)+\mathrm{th}(b)}{1-\mathrm{th}(a)\mathrm{th}(b)}$ diff --git a/topologie discrète.md b/topologie discrète.md new file mode 100644 index 00000000..bac0ed9e --- /dev/null +++ b/topologie discrète.md @@ -0,0 +1,26 @@ +--- +up: + - "[[structure de topologie|topologie]]" +tags: + - s/maths/topologie +aliases: +--- + +> [!definition] [[topologie discrète]] +> Soit $E$ un ensemble +> La **topologie discrète** sur $E$ est la topologie pour laquelle +> $\forall x \in E,\quad \{ x \} \text{ est un ouvert}$ +> - I la +^definition + +# Propriétés + +> [!proposition]+ les ouverts sont les fermés +> Tout ouvert de la topologie discrète sur un ensemble est aussi un fermé. +> > [!démonstration]- Démonstration +> > Soit $U$ un ouvert de la topologie discrète sur un ensemble $X$ +> > $X \setminus U \subseteq X$ donc est un ouvert +> > $U = X \setminus ($ + +# Exemples + diff --git a/topologie engendrée.md b/topologie engendrée.md index cf20e112..9a8e6e03 100644 --- a/topologie engendrée.md +++ b/topologie engendrée.md @@ -7,15 +7,18 @@ aliases: --- > [!definition] [[topologie engendrée]] -> Soit $X$ un ensemble et $B$ un ensemble de sous-ensembles de $X$ tel que $X \in B$ et stable par intersection finie. -> Alors toutes les unions de membres de $B$ forment une topologie sur $X$, qu'on appelle topologie engendrée par $B$ -> --- > Soit $X$ un ensemble -> Soit $B \subset \mathscr{P}(X)$ +> Soit $B \subset \mathscr{P}(X)$ tel que : +> - $X \in B$ +> - $\forall A_1, A_2 \in B,\quad A_1 \cap A_2 \in B$ ($B$ est stable par intersection finie) +> +> --- +> Soit $X$ un ensemble et $B$ un ensemble de sous-ensembles de $X$ tel que $X \in B$ et stable par intersection finie. +> Alors toutes les unions de membres de $B$ forment une [[structure de topologie|topologie]] sur $X$, qu'on appelle topologie engendrée par $B$ +> ^definition # Propriétés # Exemples - diff --git a/topologie grossière.md b/topologie grossière.md new file mode 100644 index 00000000..8decefae --- /dev/null +++ b/topologie grossière.md @@ -0,0 +1,17 @@ +--- +up: + - "[[structure de topologie|topologie]]" +tags: + - s/maths/topologie +aliases: +--- + +> [!definition] [[topologie grossière]] +> Soit $E$ un ensemble +> La **topologie grossière sur $E$** est la [[structure de topologie|topologie]] sur $E$ dont les seuls ouverts sont $\emptyset$ et $E$ +^definition + +# Propriétés + +# Exemples +