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Indicator sequences and indicator topologies of Fort transformation groups

Fatemah Ayatollah Zadeh Shirazi, Fatemeh Ebrahimifar

Abstract

In the following text we prove that there exists a Fort transformation group with indicator sequence $(p_0,\ldots,p_n)$ if and only if $0=p_0\leq p_1\leq\cdots\leq p_n=1$, moreover we characterize all possible indicator topological spaces of Fort transformation groups.The text will study indicator sequences and indicator topologies of Fort transformation semigroups too.

Indicator sequences and indicator topologies of Fort transformation groups

Abstract

In the following text we prove that there exists a Fort transformation group with indicator sequence if and only if , moreover we characterize all possible indicator topological spaces of Fort transformation groups.The text will study indicator sequences and indicator topologies of Fort transformation semigroups too.

Paper Structure

This paper contains 4 sections, 9 theorems, 16 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Indicator sequences and indicator topologies of Fort transformation groups with finite height
  4. Indicator sequences and indicator topologies of Fort transformation semigroups with finite height

Key Result

Lemma 3.1

In infinite Fort transformation group $(X,S)$ for all $x\in X$, the following statements are equivalent:

Theorems & Definitions (18)

  • Remark 2.1
  • Lemma 3.1
  • proof
  • Lemma 3.2
  • proof
  • Theorem 3.3
  • proof
  • Theorem 3.4
  • proof
  • Corollary 3.5
  • ...and 8 more