WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 25, 2026
A New Perspective on Compactness via D-Sets in Bitopological Spaces
Authors: ,
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Abstract: This paper presents fundamental concepts and general examples of D-sets, along with numerous facts and properties about them. It also discusses the concept of D-compactness in topological spaces, as well as compactness in bitopological spaces, and several theories related to these concepts. Here, we examine the concept of D-compactness in bitopological spaces, providing various definitions and examples to illustrate the main ideas, facts, and theories. Our discussion deals with special types of covering properties, namely the concept of compactness in bitopological spaces, including. P*-D-compactness and S*-D- compactness. We examine the main properties of these concepts and how these properties relate to each other through established relationships with illustrative examples supporting these ideas.
Keywords:
D-sets, $$\tau_1^{*}\tau_2^{*}$$-D-cover, $$P^{*}$$-D-cover, $$P^{*}$$-D-compact, $$S^{*}$$-D-compact, $$P^{*}$$-continuous function, $$P^{*}$$-open function, $$P^{*}$$-closed function, $$P^{*}$$-homeomorphism
Pages: 252-259
DOI: 10.37394/23206.2026.25.25