versão impressa ISSN 0716-0917
Proyecciones (Antofagasta) v.24 n.1 Antofagasta maio 2005
SEQUENTIAL S*-COMPACTNESS IN L-TOPOLOGICAL SPACES*
In this paper, a new notion of sequential compactness is introduced in L-topological spaces, which is called sequentially S*-compactness.
If L = [0, 1], sequential ultra-compactness, sequential N-compactness and sequential strong compactness imply sequential S*-compactness, and sequential S*-compactness implies sequential F-compactness. The intersection of a sequentially S*-compact L-set and a closed L-set is sequentially S*-compact. The continuous image of an sequentially S*-compact L-set is sequentially S*-compact. A weakly induced L-space (X, T ) is sequentially S*-compact if and only if (X, [T ]) is sequential compact. The countable product of sequential S*-compact L-sets is sequentially S*-compact.
Key Words and Phrases: L-topology, constant a-sequence, weak O-cluster point, weak O-limit point, sequentially S*-compactness
2000 Math. Subject Classification: Primary: 54A40.
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Received : January 2005, Accepted : March 2005.