Abstract
In this paper, we give characterizations of separation criteria for bitopological spaces via \(ij\)-continuity. We show that if a bitopological space is a separation axiom space, then that separation axiom space exhibits both topological and heredity properties. For instance, let \((X, \tau_{1}, \tau_{2})\) be a \(T_{0}\) space then, the property of \(T_{0}\) is topological and hereditary. Similarly, when \((X, \tau_{1}, \tau_{2})\) is a \(T_{1}\) space then the property of \(T_{1}\) is topological and hereditary. Next, we show that separation axiom \(T_{0}\) implies separation axiom \(T_{1}\) which also implies separation axiom \(T_{2}\) and the converse is true.
Highlights
S tudies have been conducted by different authors on continuity and its aspects
Many results have so far been obtained. Most of these results have been successfully obtained by use of separation criteria. This can be done by choosing a topological space that one may wish to use in testing a property of either topological or bitopological space
Separation axioms involve the use of spaces which distinguish disjoint sets and distinct points
Summary
S tudies have been conducted by different authors on continuity and its aspects. Many results have so far been obtained. Rupaya and Hossan [5] have shown some of the results of heredity property exhibited by some separation axioms as given below: In [5, Theorem 3.1], it was proved that if (X, τ1, τ2) is a bitopological space T0 is considered to have hereditary property. This result illustrates that (X, δ, τ) is a T0 space and A ⊂ X shows that (A, δ, τ) is T0 space. In 1988, Coy [8] carried out a study on some properties of bitopological spaces such as normality, separability and compactness Results indicate that they are inherited by a topology in a. In this paper we characterize separability criteria for bitopological spaces
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