| ON STRONGLY M_1-SPACES |
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| 作者姓名： | 陈必胜 吴利生 |
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| 作者单位： | Department of Mathematics，Suzhou University，Suzhou 215006，China，Department of Mathematics，Suzhou University，Suzhou 215006，China |
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| 基金项目： | The project is supported by The Natural Science Fundation of China |
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| 摘 要： | In this paper we have obtained the fallowing results: (1)A space X is strongly M1 if and only if X is a paracompact σ-space and every closed subset F of X has a σ-FCP open outer base. (2)If X is strongly M1 and F is closed in X, then the quotient space X/F is strongly M1. (3) The following propositions are equivalent; (Ⅰ) Every closed image of any strongly M1-space is srongly M1. (Ⅱ) In every closed image of any strongly M1-space, each point has a (σ)-FCP open neibourhood (briefly, nbd)base.
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| 关 键 词： | M1-空间 FCP 子集 线性空间 |
ON STRONGLY M1-SPACES |
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| Chen Bisheng Wu Lisheng.ON STRONGLY M_1-SPACES[J].Journal of Suzhou University(Natural Science),1994,10(2):75-80. |
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| Authors: | Chen Bisheng Wu Lisheng |
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| Institution: | DepartmentofMashematics,SuzhouUniversity,Suzhou215006,China |
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| Abstract: | In this paper we have obtained the following results:
(1) space X is strongly M1 if and only if X is a paracmnpact a-space and every closed subset F of X has a a-FCPopen outer base..
(2)If X is strongly MI and F is closed in X,then the quotient space X/F is strongly M1.
(3)The folio-wing propositions are. equivalent:
(I)Every closed, image of any strongly MI-space is strongly M1.
(II)In every closed, image of any strongly M1-space,each point has a -FCP open neibourhood (briefly ,nbd}base. |
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| Keywords: | FCP family a-FCP family strongly M1-spaces |
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