<abstract xmlns="http://www.w3.org/1999/xhtml"> In this article we prove the Tietze extension theorem for an arbitrary convex compact subset of εn with a non-empty interior. This theorem states that, if T is a normal topological space, X is a closed subset of T, and A is a convex compact subset of εn with a non-empty interior, then a continuous function f : X → A can be extended to a continuous function g : T → εn. Additionally we show that a subset A is replaceable by an arbitrary subset of a topological space that is homeomorphic with a convex compact subset of En with a non-empty interior. This article is based on [20]; [23] and [22] can also serve as reference books.</abstract>

In this article we prove the Tietze extension theorem for an arbitrary convex compact subset of εn with a non-empty interior. This theorem states that, if T is a normal topological space, X is a closed subset of T, and A is a convex compact subset of εn with a non-empty interior, then a continuous function f : X → A can be extended to a continuous function g : T → εn. Additionally we show that a subset A is replaceable by an arbitrary subset of a topological space that is homeomorphic with a convex compact subset of En with a non-empty interior. This article is based on [20]; [23] and [22] can also serve as reference books.

Tietze Extension Theorem for n-dimensional Spaces

Institute of Informatics University of Białystok Sosnowa 64, 15-887 Białystok Poland

Formalized Mathematics

This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License. (CC BY-SA 3.0)

{"article-title":"Tietze Extension Theorem for n-dimensional Spaces"}

In this article we prove the Tietze extension theorem for an arbitrary convex compact subset of εn with a non-empty interior. This theorem states that, if T is...

Tietze Extension Theorem for n-dimensional Spaces

Published Online: Mar 30, 2014

Page range: 11 - 19

DOI: https://doi.org/10.2478/forma-2014-0002

Keywords
Tietze extension, hypercube

© by Karol Pąk

This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License. (CC BY-SA 3.0)

Tietze Extension Theorem for n-dimensional Spaces

Published Online: Mar 30, 2014

Page range: 11 - 19

DOI: https://doi.org/10.2478/forma-2014-0002

KeywordsTietze extension, hypercube

© by Karol Pąk

This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License. (CC BY-SA 3.0)

Keywords
Tietze extension, hypercube