POINTWISE CONTINUOUS SHADOWING AND STABILITY IN GROUP ACTIONS

Let Act(G, X) be the set of all continuous actions of a finitely generated group G on a compact metric space X. In this paper, we study the concepts of topologically stable points and continuous shadowable points of a group action T ∈ Act(G, X). We show that if T is expansive then the set of continuous shadowable points is contained in the set of topologically stable points.

1. Introduction

2. Preliminaries

3. Continuous shadowable points

4. Topologically stable points

5. The proof of main theorem

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