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Quasi θ-spaces and pairwise θ-perfect irreducible mappings

Part of: Maps and general types of spaces defined by maps Spaces with richer structures

Published online by Cambridge University Press:  09 April 2009

A. Kandil ,
E. E. Kerre ,
M. E. El-Shafei  and
A. A. Nouh
A. Kandil
Affiliation:
Benha University, Egypt
E. E. Kerre
Affiliation:
Seminar for Mathematics Analysis
M. E. El-Shafei
Affiliation:
State University of Gent, Belgium
A. A. Nouh
Affiliation:
Mansoura University, Egypt
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Abstract

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In this paper we extend the notion of perfect, θ-continuous, irreducible and θ-perfect mappings to bitopological spaces. The main result is the following: the (small) image of an (i, j)-canonical open sets is an (i, j)-canonical open set under a pairwise θ-closed irreducible surjective mapping. Also we extend the notion of θ-proximity spaces to quasi θ-proximity spaces and point out the interrelation between it and separated quasi-proximity spaces by means of a pairwise θ-perfect irreducible mappings.

MSC classification

Secondary: 54C10: Special maps on topological spaces (open, closed, perfect, etc.) 54E05: Proximity structures and generalizations 54E55: Bitopologies
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 52 , Issue 3 , June 1992 , pp. 322 - 333
Copyright
Copyright © Australian Mathematical Society 1992

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