International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 2, Pages 303-310
doi: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 Robert A. Herrmann. 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.