From 55e29f03ac3b537843f85892a1323e1f46321675 Mon Sep 17 00:00:00 2001 From: Preston Pan Date: Sat, 11 Apr 2026 13:14:04 -0700 Subject: new articles and snippets --- mindmap/neighbourhood.org | 15 +++++++++++++++ 1 file changed, 15 insertions(+) create mode 100644 mindmap/neighbourhood.org (limited to 'mindmap/neighbourhood.org') diff --git a/mindmap/neighbourhood.org b/mindmap/neighbourhood.org new file mode 100644 index 0000000..f7014e5 --- /dev/null +++ b/mindmap/neighbourhood.org @@ -0,0 +1,15 @@ +:PROPERTIES: +:ID: e4ac2e89-1975-40de-9d6a-98281a3ca83e +:ROAM_ALIASES: "compact neighbourhood" "closed neighbourhood" "open neighbourhood" "open neighborhood" +:END: +#+title: Neighbourhood +#+author: Preston Pan +#+description: Locality in topological spaces. +#+options: broken-links:t + +* Introduction +A /neighbourhood/ $N$ of a point $x$ in a topological space $X$ is defined as a set in a topological space which contains an open set $U$ containing +the point $x$. + +Often times it is useful for defining [[id:122fd244-ffeb-47d0-89ce-bf9bc6f01b70][limit]] behavior on the topology. An /open neighbourhood/ is a neighbourhood which is also an open set, and a +compact and closed neighbourhood follows those same naming conventions, respectively. -- cgit v1.3