On topological groups via a-local functions

Wadei Al-Omeri, Mohd. Salmi Md. Noorani, Ahmad Al-Omari

Research output: Contribution to journalArticle

Abstract

An ideal on a set X is a nonempty collection of subsets of X which satisfies the following conditions (1)A ∈ I and B ⊂ A implies B ∈ I; (2) A ∈ I and B ∈ I implies A ∪ B ∈ I. Given a topological space (X,τ) an ideal I on X and A ⊂ X, Ra(A) is defined as ∪{U ∈ a: U - A ∈ I}, where the family of all a-open sets of X forms a topology [5, 6], denoted by τa. A topology, denoted τa*, finer than τa is generated by the basis β(I,τ) = {V - I: V ∈ τa(x), I ∈ I}, and a topology, denoted 〈Ra(τ)〉 coarser than τa is generated by the basis Ra(τ) = {Ra(U): U ∈ τa}. In this paper A bijection f: (X,τ,I) → (X,σ,J) is called a A*-homeomorphism if f: (X,τa*) → (Y,σa*) is a homeomorphism, Ra-homeomorphism if f: (X,Ra(τ)) → (Y,Ra(σ)) is a homeomorphism. Properties preserved by A*-homeomorphism are studied as well as necessary and sufficient conditions for a Ra-homeomorphism to be a A*-homeomorphism.

Original languageEnglish
Pages (from-to)33-42
Number of pages10
JournalApplied General Topology
Volume15
Issue number1
DOIs
Publication statusPublished - 2014

Fingerprint

Topological group
Homeomorphism
Topology
Imply
Bijection
Open set
Topological space
Necessary Conditions
Subset
Sufficient Conditions

Keywords

  • A*-homeomorphism
  • a-local function
  • Ideal spaces
  • Topological groups

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

On topological groups via a-local functions. / Al-Omeri, Wadei; Md. Noorani, Mohd. Salmi; Al-Omari, Ahmad.

In: Applied General Topology, Vol. 15, No. 1, 2014, p. 33-42.

Research output: Contribution to journalArticle

Al-Omeri, Wadei ; Md. Noorani, Mohd. Salmi ; Al-Omari, Ahmad. / On topological groups via a-local functions. In: Applied General Topology. 2014 ; Vol. 15, No. 1. pp. 33-42.
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