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 r...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.展开更多
基金Supported by the Department of Education Sichuan Province Foundation for Science Research(2006C041)
文摘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.
