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equivariant Tietze extension theorem

Contents

Context

Topology

topology (point-set topology, point-free topology)

see also differential topology, algebraic topology, functional analysis and topological homotopy theory

Introduction

Basic concepts

Universal constructions

Extra stuff, structure, properties

Examples

Basic statements

Theorems

Analysis Theorems

topological homotopy theory

Representation theory

Homotopy theory

homotopy theory, (∞,1)-category theory, homotopy type theory

flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed

models: topological, simplicial, localic, …

see also algebraic topology

Introductions

Definitions

Paths and cylinders

Homotopy groups

Basic facts

Theorems

Contents

Idea

A generalization of the Tietze extension theorem to equivariant functions provides conditions under which a continuous and equivariant function from a subspace of a topological G-space to another topological G-space has an extension to a continuous and equivariant function to the full GG-space.

Statement

Theorem

(Tietze-Gleason extension theorem)

Let

If

or

then ff has an extension to an equivariant continuous function f^\widehat f on all of XX.

A f E f^ X \array{ A &\overset{f}{\longrightarrow}& E \\ \cap & \nearrow_{\mathrlap{ \widehat{f} }} \\ X }

(Gleason 50, see Palais 60, Theorem 1.4.3)

extension theoremscontinuous functionssmooth functions
plain functionsTietze extension theoremWhitney extension theorem
equivariant functionsequivariant Tietze extension theorem

References

Last revised on August 20, 2019 at 16:08:10. See the history of this page for a list of all contributions to it.