Two classes of locally compact sober spaces | Zendy

Karim Belaïd | Zendy; Othman Echi | Zendy; Riyadh Gargouri | Zendy

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Two classes of locally compact sober spaces

Author(s) -

Karim Belaïd,

Othman Echi,

Riyadh Gargouri

Publication year - 2005

Publication title -

international journal of mathematics and mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.21

H-Index - 39

eISSN - 1687-0425

pISSN - 0161-1712

DOI - 10.1155/ijmms.2005.2421

Subject(s) - mathematics , locally compact space , class (philosophy) , pure mathematics , compact space , space (punctuation) , locally compact group , compact open topology , point (geometry) , topological tensor product , compact operator on hilbert space , functional analysis , extension (predicate logic) , compact operator , geometry , computer science , biochemistry , chemistry , artificial intelligence , gene , programming language , operating system

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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