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2010•Shuxue jikanRequires access

Base-mesocompact Spaces

Cao Jin-wen

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Abstract

In this paper the notation of base-mesocompactness is introduced and the following results are mainly obtained:(1) Let X be base-mesocompact and X' an F σ subset of X.If X is normal,then X' is base-mesocompact relative to X.(2) Let f:X → Y be a base-mesocompact mapping,ω(X) be a regular cardinality of X and ω(X) ≥ ω(Y).If Y is base-mesocompact and regular,then X is base-mesocompact.(3) Let f:X → Y be a closed lindelof mapping with regular domain and regular range.If Y is base-mesocompact,then X is base-mesocompact.(4) Let X be base-mesocompact.If Y is locally compact and base-mesocompact,then X × Y is base-mesocompact.

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What this paper is about

In this paper the notation of base-mesocompactness is introduced and the following results are mainly obtained:(1) Let X be base-mesocompact and X' an F σ subset of X.If X is normal,then X' is base-mesocompact relative to X.(2) Let f:X → Y be a base-mesocompact mapping,ω(X) be a regular cardinality of X and ω(X) ≥ ω(Y).If Y is base-mesocompact and regular,then X is base-mesocompact.(3) Let f:X → Y be a closed lindelof mapping with regular domain and regular range.If Y is base-mesocompact,then X is base-mesocompact.(4) Let X be base-mesocompact.If Y is locally compact and base-mesocompact,then X × Y is base-mesocompact.

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Available abstract

In this paper the notation of base-mesocompactness is introduced and the following results are mainly obtained:(1) Let X be base-mesocompact and X' an F σ subset of X.If X is normal,then X' is base-mesocompact relative to X.(2) Let f:X → Y be a base-mesocompact mapping,ω(X) be a regular cardinality of X and ω(X) ≥ ω(Y).If Y is base-mesocompact and regular,then X is base-mesocompact.(3) Let f:X → Y be a closed lindelof mapping with regular domain and regular range.If Y is base-mesocompact,then X is base-mesocompact.(4) Let X be base-mesocompact.If Y is locally compact and base-mesocompact,then X × Y is base-mesocompact.

Key concepts: Base (topology), Mathematics, Base change, Cardinality (data modeling), Combinatorics, Domain (mathematical analysis), Discrete mathematics, Mathematical analysis

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