Tietze Extension Theorem for n-dimensional Spaces

Karol Pąk

Formalized Mathematics (2014)

  • Volume: 22, Issue: 1, page 11-19
  • ISSN: 1426-2630

Abstract

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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.

How to cite

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Karol Pąk. "Tietze Extension Theorem for n-dimensional Spaces." Formalized Mathematics 22.1 (2014): 11-19. <http://eudml.org/doc/267208>.

@article{KarolPąk2014,
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.},
author = {Karol Pąk},
journal = {Formalized Mathematics},
keywords = {Tietze extension; hypercube},
language = {eng},
number = {1},
pages = {11-19},
title = {Tietze Extension Theorem for n-dimensional Spaces},
url = {http://eudml.org/doc/267208},
volume = {22},
year = {2014},
}

TY - JOUR
AU - Karol Pąk
TI - Tietze Extension Theorem for n-dimensional Spaces
JO - Formalized Mathematics
PY - 2014
VL - 22
IS - 1
SP - 11
EP - 19
AB - 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.
LA - eng
KW - Tietze extension; hypercube
UR - http://eudml.org/doc/267208
ER -

References

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