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The existence of suitable sets in locally compact strongly topological gyrogroups

Jiajia Yang, Jiamin He, Fucai Lin

Abstract

A subset $S$ of a topological gyrogroup $G$ is said to be a {\it suitable set} for $G$ if $S$ is discrete, the gyrogroup generated by $S$ is dense in $G$, and $S\cup \{0\}$ is closed in $G$, where $0$ is the identity element of $G$. In this paper, it is proved that every locally compact strongly topological gyrogroup has a suitable set, which gives an affirmative answer to a question posed by F. Lin, et al. in \cite{key14}.

The existence of suitable sets in locally compact strongly topological gyrogroups

Abstract

A subset of a topological gyrogroup is said to be a {\it suitable set} for if is discrete, the gyrogroup generated by is dense in , and is closed in , where is the identity element of . In this paper, it is proved that every locally compact strongly topological gyrogroup has a suitable set, which gives an affirmative answer to a question posed by F. Lin, et al. in \cite{key14}.

Paper Structure

This paper contains 2 sections, 16 theorems, 18 equations.

Table of Contents

  1. Introduction and Preliminaries
  2. Locally compact strongly topological gyrogroup

Key Result

Lemma 2.1

key13 Let $(G, \tau, \oplus)$ be a topological gyrogroup and $H$ is a locally compact subgyrogroup of $G$, then $H$ is closed in $G$.

Theorems & Definitions (31)

  • Definition 1.2
  • Definition 1.3
  • Definition 1.4
  • Definition 1.5
  • Definition 1.6
  • Definition 1.7
  • Definition 1.8
  • Lemma 2.1
  • Lemma 2.2
  • proof
  • ...and 21 more