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Connection Properties in Nearness Spaces

Published online by Cambridge University Press:  20 November 2018

D. Baboolal
Affiliation:
Department of Mathematics, University of Durban-WestvillePrivate Bag X54001 Durban 4000, South Africa
H. L. Bentley
Affiliation:
Department of Mathematics, University of Durban-WestvillePrivate Bag X54001 Durban 4000, South Africa
R. G. Ori
Affiliation:
Department of Mathematics, University of Durban-WestvillePrivate Bag X54001 Durban 4000, South Africa Department of Mathematics, University of ToledoToledo, Ohio 43606 U.S.A.
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Abstract

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We prove that a topological space X has a locally connected regular T1, extension if and only if X is the underlying topological space of a nearness space Y which is concrete, regular and uniformly locally uniformly connected.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1985

References

1. Baboolal, D., On some uniform connection properties related to local connectedness, Quaestiones Mathematicae, to appear.Google Scholar
2. Bentley, H.L., Normal nearness spaces, Quaestiones Mathematicae 2 (1977), pp. 23—24.Google Scholar
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5. Herrlich, H., On the extendibility of continuous functions, General Topology Appl. 5 (1974), pp. 213215.Google Scholar
6. Herrlich, H., Topological Structures, Math. Centre Tract (Amsterdam) 52 (1974), pp. 59122.Google Scholar
7. Preuss, G., Connectedness and disconnectedness in S-Near, Lecture notes in Math., (Springer-Verlag) 915 (1982), pp. 275292.Google Scholar
8. Gleason, A.M., Universal locally connected refinements, Illinois J. Math. 7 (1963), pp. 521—531.Google Scholar
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