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International Journal of Mathematics and Mathematical Sciences
Volume 7, Issue 2, Pages 303-310
http://dx.doi.org/10.1155/S0161171284000326

Preconvergence compactness and P-closed spaces

Mathematics Department, U. S. Naval Academy, Annapolis 21402, Maryland, USA

Received 11 February 1983; Revised 11 June 1983

Copyright © 1984 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this article the major result characterizes preconvergence compactness in terms of the preconvergence closedness of second projections. Applying this result to a topological space (X,T) yields similar characterizations for H-closed, nearly compact, completely Hausdorff-closed, extremely disconnected Hausdorff-closed, Urysohn-closed, S-closed and R-closed spaces, among others. Moreover, it is established that the s-convergence of Thompson (i.e. rc-convergence) is equivalent to topological convergence where the topology has as a subbase the set of all regular-closed elements of T.