The near compactness of nearly countably compact spaces
by
G. B. Navalagi
Department of Mathematics, G.H.College, Haveri-581110 Karnataka, India

In 1970, Philip.Bacon [ PJM 32(3), (1970), 587-592 ] has defined and studied the compactness of the countably compact spaces, namely, isocompactness in topology:

A space X is called isocompact if each of its closed countably compact subsets is compact. Since then many authors have been contributed to the theory of isocompactness.

In the literature, N-closed subsets are defined and studied by D.A.Carnahan [Boll. UMI., (4), 6(1972), 146-153], a subset A of a space X is called N-closed if every covering of a with regular open subsets of the space has a finite subcovering and nearly compact spaces have been studied by Singal and Mathur [Boll. UMI., (4), 2(1969), 702-710], a space X is called nearly compact if X is N-closed. In 1980, N.Ergun [Istanbul .Univ. Fen.Mec.Ser. A, 45 (1980), 65-87] has defined the concept of nearly countably compact spaces in topology, a space X is called nearly countably compact if every countable regular open cover of X has a finite subcover. In this paper, we introduce the concepts of iso-nearly compact spaces, hereditarily isonearly compact spaces, CL-isonearly compact spaces and hereditarily CL-isonearly compact spaces using nearly countably compact and nearly compact subsets : (i) A space X is called isonearly compact if each of its closed nearly countably compact subsets is nearly compact; (ii) A space X is called hereditarily isonearly compact if every subspace of X is isonearly compact space; (iii) A space X is called CL-isonearly compact if the closure of each nearly countably compact subset of X is nearly compact and (iv) A space X is called hereditarily CL-isonearly compact if every subspace of X is CL-isonearly compact space. We also, define nearly countably compact and nearly compact mappings: A continuous map f:X --> Y is called nearly countably compact (resp. nearly compact) if f^-1(y) is nearly countably compact (resp. nearly compact) for each point y in Y. Among other things, we proved the many basic properties of these spaces and studied some comparision w.r.t to isocompactness.

Date received: June 23, 2000

Copyright © 2000 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 # caeu-46.