On Murayama's theorem on extensor properties of G-spaces of given orbit types

TL;DR

This paper introduces a new method for extending actions of compact transformation groups and applies it to analyze how equivariant extensor properties are preserved within specific orbit type subspaces.

Contribution

It develops a novel method for extending group actions and investigates the preservation of equivariant extensor properties in orbit type subspaces.

Findings

Method successfully extends actions of compact groups

Preservation of equivariant extensor properties established

Applicable to various orbit type subspaces

Abstract

We develop a method of extending actions of compact transformation groups which is then applied to the problem of preservation of equivariant extensor property by passing to a subspace of given orbit types.