Preconvergence compactness and P-closed spaces

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.

Keywords

• convergence spaces
• preconvergence spaces
• H-closed
• nearly compact
• completely Hausdorff-closed
• EDH-closed
• Urysohn-closed
• S-closed
• R-closed.