Regularity and normality in ideal bitopological spaces

Néstor Raúl Pachón Rubiano

doi:10.22199/issn.0717-6279-2021-02-0026

Abstract

We introduce, and study, the regularity and normality in ideal bitopological spaces, absent subject in literature. Our definitions have the advantage of using only the open sets of the two underlying topologies. These new concepts represent generalizations of Kelly’s concepts of pairwise regularity and pairwise normality. The extension of the T0, T1 and T2 axioms to these spaces is due to Caldas et al.

Highlights

Introduction and preliminariesBitopological spaces were introduced in 1963 by J
[2], as a tool to systematize the study of quasi-metrics
Regarding the study of the axioms of separation in ideal bitopological spaces, Caldas, Jafari, Popa and Rajesh, in a joint work of 2010, have defined what refers to the axioms T0, T1 and T2

Summary

Introduction and preliminaries

Bitopological spaces were introduced in 1963 by J. In this paper we introduce and investigate the pairwise I-regular spaces, the pairwise I-normal spaces, the strongly pairwise I-regular spaces and the strongly pairwise I-normal spaces, and for this we only use the open sets of the underlying topologies. This is more natural but it allows us to work in a simpler way. It is very simple to prove that Ii is an ideal in Xi. If τ and β are topologies in a set X, (X, τ, β) is called a bitopological space [2]. The symbol 2 is used to indicate the end of a proof

Pairwise I-regular spaces

Pairwise I-normal spaces

Strongly pairwise I-regular spaces