Two classes of locally compact sober spaces

Karim Belaid, Othman Echi and Riyadh Gargouri

International Journal of Mathematics and Mathematical Sciences, 2005, vol. 2005, 1-7

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.

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:367623

DOI: 10.1155/IJMMS.2005.2421

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