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totally paracompact をテンプレートにして作成
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開始行:
*Definition 1 [#wdf2aadb]
A space is said to be totally paracompact if every open base has a [[locally finite]] subfamily covering the space.
*Definition 2 [#m6f77788]
Let X be a topological space and let Y be its subset.
Y is called totally paracompact with respect to X if every outer base contains a X-[[locally finite]] cover. A family B of open sets in X is called an outer cover if, for every point y in Y and every open set G in X, there is some member V
*Remark [#z78d3c6a]
-For Definition 1, it is also called [[basically paracompact]]
*Reference [#t52a4a9f]
:Definition 1|
R. M. Ford, ''Basic properties in dimension theory'', Dissertation, Auburn University, 1963.
M. K. Singal, ''Some Generalizations of Paracompactness'', Proceedings of the Kanpur topological conference, 1968. Academia Publishing House of the Czechoslovak Academy of Sciences, Praha, 1971. pp. 245-263.
:Definition 2|
R. Telgarsky and H. Kok, ''The space of rationals is not absolutely paracompact'', Fund. Math. 73 (1971), 75-78.
終了行:
*Definition 1 [#wdf2aadb]
A space is said to be totally paracompact if every open base has a [[locally finite]] subfamily covering the space.
*Definition 2 [#m6f77788]
Let X be a topological space and let Y be its subset.
Y is called totally paracompact with respect to X if every outer base contains a X-[[locally finite]] cover. A family B of open sets in X is called an outer cover if, for every point y in Y and every open set G in X, there is some member V
*Remark [#z78d3c6a]
-For Definition 1, it is also called [[basically paracompact]]
*Reference [#t52a4a9f]
:Definition 1|
R. M. Ford, ''Basic properties in dimension theory'', Dissertation, Auburn University, 1963.
M. K. Singal, ''Some Generalizations of Paracompactness'', Proceedings of the Kanpur topological conference, 1968. Academia Publishing House of the Czechoslovak Academy of Sciences, Praha, 1971. pp. 245-263.
:Definition 2|
R. Telgarsky and H. Kok, ''The space of rationals is not absolutely paracompact'', Fund. Math. 73 (1971), 75-78.
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