# Tietze Extension Theorem for n-dimensional Spaces

Formalized Mathematics (2014)

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

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topKarol 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 -

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