Tietze Extension Theorem for n-dimensional Spaces

• Autorzy: Karol Pąk
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Tietze extension; hypercube

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2014
• Tom: 22
• Numer: 1
• Strony: 11-19

Twórcy

autor

Karol Pąk

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

Bibliografia

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Identyfikatory

DOI

10.2478/forma-2014-0002