Countable s*-compactness in L-spaces
DOI:
https://doi.org/10.4067/S0716-09172005000300007Keywords:
L-topology, βa-open cover, Qa-open cover, S∗-compactness, countable S∗-compactness.Abstract
In this paper, the notions of countable S*-compactness is introduced in L-topological spaces based on the notion of S*-compactness. An S*-compact L-set is countably S*-compact. If L = [0, 1], then countable strong compactness implies countable S*-compactness and countable S*-compactness implies countable F-compactness, but each inverse is not true. The intersection of a countably S*-compact L-set and a closed L-set is countably S*-compact. The continuous image of a countably S*-compact L-set is countably S*-compact. A weakly induced L-space (X, T ) is countably S*-compact if and only if (X, [T ]) is countably compact.
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