Heine–Borel theorem
id:
heine-borel-theorem-169-7846009
title:
Heine–Borel theorem
text:
In real analysis the Heine–Borel theorem, named after Eduard Heine and Émile Borel, states: For a subset S of Euclidean space Rn, the following two statements are equivalent:
- S is compact, that is, every open cover of S has a finite subcover
- S is closed and bounded.
brand slug:
wiki
category slug:
encyclopedia
description:
Subset of Euclidean space is compact if and only if it is closed and bounded
original url:
https://en.wikipedia.org/wiki/Heine%E2%80%93Borel_theorem
date created:
2001-11-30T19:35:45Z
date modified:
2024-08-31T12:59:54Z
main entity:
{"identifier":"Q253214","url":"https://www.wikidata.org/entity/Q253214"}
image:
fields total:
13
integrity:
15