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International Journal of Mathematics and Mathematical Sciences
Volume 13, Issue 1, Pages 55-59
http://dx.doi.org/10.1155/S0161171290000084

On weaker forms of compactness Lindelöfness and countable compactness

Department of Mathematics, University of Durban-Westville, Private Bag X54001, Durban 4000, South Africa

Received 6 July 1987; Revised 9 August 1988

Copyright © 1990 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

A theory of e-countable compactness and e-Lindelöfness which are weaker than the concepts of countable compactness and Lindelöfness respectively is developed. Amongst other results we show that an e-countably compact space is pseudocompact, and an example of a space which is pseudocompact but not e-countably compact with respect to any dense set is presented. We also show that every e-Lindelöf metric space is separable.