刘川.关于点可数覆盖[J].数学研究及应用,1996,16(1):121~124 |
关于点可数覆盖 |
On Point-Countable Covers |
投稿时间:1993-03-16 修订日期:1995-07-01 |
DOI:10.3770/j.issn:1000-341X.1996.01.024 |
中文关键词: k-网 cs*-网 点可数 s-映射 伪开映射 商映射. |
英文关键词:k -network cs*-network s-mapping point-countable pseudo-open mapping quotient mapping. |
基金项目:国家自然科学基金资助课题. |
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中文摘要: |
本文证明了(1)具有点可数基空间的商s-像X有点可数基的充要条件是X是q-空间;(2)度量空间的伪开s-像若满足条件(*),则它在伪开s-映射下是保持的,(3)给出反例否定地回答了[1]和[2]中的问题. |
英文摘要: |
We prove the following results: (1) A qustient s -images of spaces with a point-countable base has a point-countable base if and only if it is a q-space. (2) A pseudo-open s-image of metric space is preserved by pseudo-open s -mapping under the condition (*). (3) A example is given to answer the questions in [1] and [2] in the negative. |
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