Bi-topological spaces
- UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
- Betty Ruffin Garner (Creator)
- Institution
- The University of North Carolina at Greensboro (UNCG )
- Web Site: http://library.uncg.edu/
- Advisor
- 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.
Bi-topological spaces
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Created on 1/1/1971
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Additional Information
- Publication
- Thesis
- Language: English
- Date: 1971
- Subjects
- Topological spaces
- Set theory.