International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 1, Pages 55-59
doi:10.1155/S0161171290000084
On weaker forms of compactness, Lindelöfness, and countable compactness
D. Baboolal
, J. Backhouse
and R.G. Ori
Department of Mathematics, University of Durban-Westville, Private Bag X54001, Durban 4000, South Africa
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.