The lower and upper topologies as a bitopology

Authors

  • B. Dvalishvili Faculty of Mechanics and Mathematics, I. Javakhishvili Tbilisi State University, 2, University St., Tbilisi 380043, Georgia. Author

Keywords:

$(l, u)$- and $(u, l)$-boundaries, a hereditarily strong normally ordered space, $l$- and $u$-nowhere dense sets, $l$- and $u$-first (second) category set, $l$- and $u$-Baire spaces

Subjects:

54F05, 54E55

Abstract

The importance of the theory of bitopological spaces is fully demonstrated by its natural relationship to the theory of ordered topological spaces. Using the parallels drawn by M. Canfell and T. McCallion between the theory of bitopological spaces and that of ordered topological spaces, we construct the dimension theory for ordered topological spaces and formulate and study the Baire-like properties of the latter spaces, thereby filling in the gap of the theory of ordered topological spaces. Further, based on these parallels, the relations between the separation axioms of ordered topological spaces and the corresponding bitopological spaces are established.

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Published

2003-04-15

Issue

Vol. 55 No. 1–2 (2003): Vol. 55, Issue 1–2

Section

Articles

License

Copyright (c) 2003 Authors retain copyright to their work.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.