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Encyclopedia of Compactness Wiki*
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shrinking をテンプレートにして作成
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*Definition [#n8bbf32c]
A topological space is said to be a shrinking space if every open cover admits a shrinking.
A shrinking of an open cover is another open cover indexed by the same indexing set, with the property that the closure of each open set in the shrinking lies inside the corresponding original open set.
*Property [#wa8ee54b]
-Every shrinking space is normal and [[countably paracompact]].
-In a normal space, every [[locally finite]], and in fact, every [[point-finite]] open cover admits a shrinking.
-Thus, every normal [[metacompact]] space is a shrinking space. In particular, every [[paracompact]] space is a shrinking space.
*Reference [#e32b4656]
http://en.wikipedia.org/wiki/Shrinking_space
終了行:
*Definition [#n8bbf32c]
A topological space is said to be a shrinking space if every open cover admits a shrinking.
A shrinking of an open cover is another open cover indexed by the same indexing set, with the property that the closure of each open set in the shrinking lies inside the corresponding original open set.
*Property [#wa8ee54b]
-Every shrinking space is normal and [[countably paracompact]].
-In a normal space, every [[locally finite]], and in fact, every [[point-finite]] open cover admits a shrinking.
-Thus, every normal [[metacompact]] space is a shrinking space. In particular, every [[paracompact]] space is a shrinking space.
*Reference [#e32b4656]
http://en.wikipedia.org/wiki/Shrinking_space
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