Sequential S∗-compactness in L-topological spaces

Shu-Ping Li

Resumen


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.


Palabras clave


L-topology ; Constant a-sequence ; Weak O-cluster point ; Weak O-limit point ; Sequentially S∗-compactness.

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DOI: http://dx.doi.org/10.4067/S0716-09172005000100001

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