Bi-topological spaces

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
Betty Ruffin Garner (Creator)
The University of North Carolina at Greensboro (UNCG )
Web Site:
Hughes Hoyle

Abstract: Kelly initiated the study of bi-topological spaces in [3]. In this paper the concepts of pairwise-T, pairwise regular, pairwise Hausdorff, quasi-pseudo-metrizable, and quasi-metrizable are introduced, and the following theorem is proved. Theorem. If (X, P, Q) is a pairwise regular bi-topological space satisfying the second axiom of countability, then (X, P, Q) is quasi-pseudo-metrizable. If in addition (X, P, Q) is pairwise Hausdorff, it is quasi-metrizable. The concepts underlying the above definitions do not easily rarry over to concepts such as pairwise compact, pairwise connected, and pairwise continuous, as is partially demonstrated in [2]. This author was therefore led to investigate other possible ways for defining properties in bi-topological spaces. One idea investigated was that of bi-open sets. A similar idea has recently been studied in [1]. It is the purpose of this paper to introduce the concept of bi-open sets in bi-topological spaces and to demonstrate how properties of topological spaces can easily be expressed for bi-topological spaces.

Additional Information

Language: English
Date: 1971
Topological spaces
Set theory.

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