Preopen sets in bispaces

TL;DR

This paper extends the concepts of preopen sets and precontinuity from topological and bitopological spaces to bispaces, analyzing how existing results adapt to this more general setting.

Contribution

It introduces the notions of pairwise preopen and precontinuous sets in bispaces and examines their properties and relationships, broadening the theoretical framework.

Findings

Generalization of preopen sets to bispaces

Analysis of pairwise precontinuity in bispaces

Comparison with results in bitopological spaces

Abstract

The notion of preopen sets and precontinuity in a topological space was introduced by Mashhour et. al in 1982 [13]. Later the same was studied in a bitopological space in [7] and [9]. Here we have studied the idea of pairwise preopen sets (semi preopen) and pairwise precontinuity (semi precontinuity) in a more general structure of a bispace and investigate how far several results as valid in a bitopological space are affected in a bispace.