Merotopic Spaces and Extensions of Closure Spaces

Chattopadhyay, K. C. ; Njåstad, Olav ; Thron, W. J.

Canadian journal of mathematics, Tome 35 (1983) no. 4, pp. 613-629

Résumé

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 T 1-extensions of a given T 1-space. She succeeded in showing that the mapping induces a 1 – 1 correspondence between the contingual nearness spaces in and the compactifications in .

Détail

DOI : 10.4153/CJM-1983-035-6

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