Two classes of locally compact sober spaces

Karim Belaid; Othman Echi; Riyadh Gargouri

doi:10.1155/IJMMS.2005.2421

Two classes of locally compact sober spaces

Karim Belaid^*
, Othman Echi
, Riyadh Gargouri

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We deal with two classes of locally compact sober spaces, namely, the class of locally spectral coherent spaces and the class of spaces in which every point has a closed spectral neighborhood (CSN-spaces, for short). We prove that locally spectral coherent spaces are precisely the coherent sober spaces with a basis of compact open sets. We also prove that CSN-spaces are exactly the locally spectral coherent spaces in which every compact open set has a compact closure.

Original language	English
Pages (from-to)	2421-2427
Number of pages	7
Journal	International Journal of Mathematics and Mathematical Sciences
Volume	2005
Issue number	15
DOIs	https://doi.org/10.1155/IJMMS.2005.2421
State	Published - 29 Sep 2005
Externally published	Yes

ASJC Scopus subject areas

Mathematics (miscellaneous)

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title = "Two classes of locally compact sober spaces",

abstract = "We deal with two classes of locally compact sober spaces, namely, the class of locally spectral coherent spaces and the class of spaces in which every point has a closed spectral neighborhood (CSN-spaces, for short). We prove that locally spectral coherent spaces are precisely the coherent sober spaces with a basis of compact open sets. We also prove that CSN-spaces are exactly the locally spectral coherent spaces in which every compact open set has a compact closure.",

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N2 - We deal with two classes of locally compact sober spaces, namely, the class of locally spectral coherent spaces and the class of spaces in which every point has a closed spectral neighborhood (CSN-spaces, for short). We prove that locally spectral coherent spaces are precisely the coherent sober spaces with a basis of compact open sets. We also prove that CSN-spaces are exactly the locally spectral coherent spaces in which every compact open set has a compact closure.

AB - We deal with two classes of locally compact sober spaces, namely, the class of locally spectral coherent spaces and the class of spaces in which every point has a closed spectral neighborhood (CSN-spaces, for short). We prove that locally spectral coherent spaces are precisely the coherent sober spaces with a basis of compact open sets. We also prove that CSN-spaces are exactly the locally spectral coherent spaces in which every compact open set has a compact closure.

UR - https://www.scopus.com/pages/publications/29144446145

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DO - 10.1155/IJMMS.2005.2421

M3 - Article

AN - SCOPUS:29144446145

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JO - International Journal of Mathematics and Mathematical Sciences

JF - International Journal of Mathematics and Mathematical Sciences

IS - 15

ER -

Two classes of locally compact sober spaces

Abstract

ASJC Scopus subject areas

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