SPN-compactness in L-topological spaces

Authors

  • Zhen-Guo Xu Beijing Institute of Technology.
  • Fu-Gui Shi Beijing Institute of Technology.

DOI:

https://doi.org/10.4067/S0716-09172006000100004

Keywords:

L-topological space, strongly preopen L-set, strongly preclosed L-set, SPN-compactness, countable SPN-compactness, the SPN-Lindel of property, espacio L-topológico, L-conjunto fuertemente pre-abierto, L-conjunto fuertemente pre-cerrado, SPN-compacidad.

Abstract

In this paper, the notions of SPN-compactness, countable SPNcompactness and the SPN-Lindelöf property are introduced in L-topological spaces by means of strongly preclosed L-sets. In an L-space, an Lset having the SPN-Lindelöf property is SPN-compact if and only if it is countably SPN-compact. (Countable) SPN-compactness implies (countable) N-compactness, the SPN-Lindelöf property implies the N-Lindelöf property, but each inverse is not true. Every L-set with finite support is SPN-compact. The intersection of an (a countable) SPN-compact L-set and a strongly preclosed L-set is (countably) SPNcompact. The strong preirresolute image of an (a countable) SPNcompact L-set is (countably) SPN-compact. Moreover SPN-compactness can be characterized by nets.

Author Biographies

Zhen-Guo Xu, Beijing Institute of Technology.

Department of Mathematics.

Fu-Gui Shi, Beijing Institute of Technology.

Department of Mathematics.

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Published

2017-05-08

How to Cite

[1]
Z.-G. Xu and F.-G. Shi, “SPN-compactness in L-topological spaces”, Proyecciones (Antofagasta, On line), vol. 25, no. 1, pp. 47-61, May 2017.

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Section

Artículos