On Generalized Bitopological Properties

Abstract

A bitopological space (X, τ1, τ2) was introduced by Kelly [38] in 1963, as a method of generalizes topological spaces (X, τ). Every bitopological space (X, τ1, τ2) can be regarded as a topological space (X, τ) if τ1 = τ2 = τ . Furthermore, he extended some of the standard results of separation axioms and mappings in a topological space to a bitopological space. The notion of connectedness in bitopological spaces has been studied by Pervin [51], Reily [52] and Swart [58]. In 1983 Mashhour et al. [42] introduced the notion of supra topological spaces by dropping only the intersection condition. Kandil et al. [35] generated a supra topological space (X, τ12) from the bitopological space (X, τ1, τ2) and studied some properties of the space (X, τ1, τ2) via properties of the associated space (X, τ12). Thereafter, a large number of papers have been written to generalize topological concepts to bitopological setting [15, 18, 20, 19, 35, 55].