Katětov–Tong insertion theorem
id:
kat-tov-tong-insertion-theorem-184-9868825
title:
Katětov–Tong insertion theorem
text:
The Katětov–Tong insertion theorem is a theorem of point-set topology proved independently by Miroslav Katětov and Hing Tong in the 1950s. The theorem states the following: Let X be a normal topological space and let g, h : X → R be functions with g upper semicontinuous, h lower semicontinuous, and g ≤ h. Then there exists a continuous function f : X → R with g ≤ f ≤ h. This theorem has a number of applications and is the first of many classical insertion theorems. In particular it implies the T
brand slug:
wiki
category slug:
encyclopedia
description:
On existence of a continuous function between semicontinuous upper and lower bounds
original url:
https://en.wikipedia.org/wiki/Kat%C4%9Btov%E2%80%93Tong_insertion_theorem
date created:
2006-07-05T18:20:20Z
date modified:
2024-09-07T07:10:56Z
main entity:
{"identifier":"Q6378601","url":"https://www.wikidata.org/entity/Q6378601"}
image:
fields total:
13
integrity:
15