Sequential S∗-compactness in L-topological spaces

• Li, Shu-Ping ^[1]
  1. [1] Mudanjiang Teachers College.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 24, Nº. 1, 2005, págs. 1-11
• Idioma: inglés
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• 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.