度量空间的序列覆盖边界紧映象(英文)  

On Sequence-covering Boundary Compact Maps of Metric Spaces

作　　者：林福财[1] 林寿[1,2] 

机构地区：[1]漳州师范学院数学系,漳州福建363000 [2]宁德师专数学系,宁德福建352100

出　　处：《数学进展》2010年第1期71-78,共8页Advances in Mathematics（China）

基　　金：Supported by the NSFC(No.10571151).

摘　　要：本文主要讨论了度量空间的序列覆盖边界紧映象.用序列商、序列覆盖或1-序列覆盖的纤维边界紧或有限来刻画具有sn网或弱基的空间.主要结果如下:(1)度量空间上的序列覆盖边界紧映射是1-序列覆盖映射;(2)空间X是度量空间的序列商边界紧映象当且仅当X是snf-第一可数空间;(3)空间X是度量空间的序列覆盖边界紧S映象当且仅当X有点可数sn-网.In this paper, we mainly discuss the images of metric spaces under sequence- covering boundary compact maps. Some spaces having certain sn-networks or weak bases are characterized by sequentially quotient maps, sequence-covering maps, or 1-sequence-covering maps that the boundary set of each fiber is finite o.r compact, The main results are that （1） Each sequence-covering and boundary compact map on a metric space is 1-sequence-covering; （2） A space X is a sequentially quotient, boundary compact image of a metric space if and only if it is an snf-countable space; （3） A space X is a sequence-covering, boundary compact and s-image of a metric space if and only if it has a point-countable sn-network.

关 键 词：序列商映射 序列覆盖映射 sn-网 弱基 

分 类 号：O189.11[理学—数学]