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Colloquium on Topology, Gyula, Hungary
August 9-15, 1998
János Bolyai Mathematical Society
Budapest, Hungary

Organizers
M. Bognár, A. Császár (chairman), J. Gerlits, I. Juhász, E. Makai, G. Moussong, R. Rimányi, L. Soukup, A. Stipsicz, J. Szenthe, A. Szücs (secretary)

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Some properties of \theta-closure spaces
by
Mila Mršević
Belgrade, Yugoslavia

Mila Mrsevi\'c (Belgrade, Yugoslavia)

SOME PROPERTIES OF   \theta-CLOSURE SPACES


Given a topological space   (X, T), the notion of   \theta-closure was introduced by Velicko in the following way: a point   x   is in the   \theta-closure of   A, denoted by   cl\thetaA, if each closed neighbourhood of   x   intersects   A. In general,   cl\theta   is not a Kuratowski closure operator since it need not be idempotent, and the pair   (X, cl\theta)   is a closure (or neighbourhood) space.

A subset   A   is   \theta-closed if   A = cl\thetaA.   \theta-closed sets are closed sets for a new topology   T\theta   on the set   X.

The semi-regularization topology of   T   is denoted by   Ts.


Various topological properties are considered on   (X, T),   (X, Ts),   (X, cl\theta)  and   (X, T\theta).

Date received: June 15, 1998

Copyright © 1998 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cabc-33.