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Strongly topologically transitive, supermixing, and hypermixing maps on general topological spaces

Mahin Ansari, Mohammad Ansari

Abstract

We give some basic properties of strongly topologically transitive, supermixing, and hypermixing maps on general topological spaces. Then we present some other results for which our mappings need to be continuous.

Strongly topologically transitive, supermixing, and hypermixing maps on general topological spaces

Abstract

We give some basic properties of strongly topologically transitive, supermixing, and hypermixing maps on general topological spaces. Then we present some other results for which our mappings need to be continuous.
Paper Structure (3 sections, 10 theorems, 11 equations)

This paper contains 3 sections, 10 theorems, 11 equations.

Table of Contents

  1. Introduction
  2. Supermixing and hypermixing maps
  3. Continuous maps

Key Result

Theorem 2.1

Let $X$ be a topological space. If there is a nontrivial finite open set $U$ in $X$, then there is no hypermixing map on $X$. In particular, if $X$ is a finite set, then, equipped with any nontrivial topology, $X$ cannot support a hypermixing map.

Theorems & Definitions (21)

  • Remark 1.1
  • Definition 1.2
  • Example 1.3
  • Theorem 2.1
  • proof
  • Proposition 2.2
  • proof
  • Proposition 2.3
  • proof
  • Proposition 2.4
  • ...and 11 more