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Merotopic Spaces and Extensions of Closure Spaces

Published online by Cambridge University Press:  20 November 2018

K. C. Chattopadhyay ,
Olav Njåstad  and
W. J. Thron
K. C. Chattopadhyay
Affiliation:
Burdwan University, Burdwan, West Bengal, India
Olav Njåstad
Affiliation:
University of Trondheim-NTH, Trondheim, Norway
W. J. Thron
Affiliation:
University of Colorado, Boulder, Boulder, Colorado
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Proximity spaces and contiguity spaces, and more recently nearness spaces, have been studied not just because they provide various approaches to uniform structure. Possibly of greater importance is that they can be used as a means of introducing compactifications and more general extensions of the topological spaces on which they are defined. Riesz [20] was probably the first to recognize this connection. Since then the idea was used by Freudenthal [9], Alexandroff [1], Smirnov [21], Leader [17] and Ivanov and Ivanova [13, 14, 15] among others.

Recently Reed [19] using work of Bentley [2, 4] and Herrlich [11, 12] studied the 1 – 1 correspondence between the class of all cluster generated nearness spaces and the class all principal T1-extensions of a given T1-space. She succeeded in showing that the mapping induces a 1 – 1 correspondence between the contingual nearness spaces in and the compactifications in .

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 35 , Issue 4 , 01 August 1983 , pp. 613 - 629
Copyright
Copyright © Canadian Mathematical Society 1983

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