ブラウザの JavaScript がオフ(ブロックまたは許可しない)に設定されているため、このページは正常に機能しません。
Encyclopedia of Compactness Wiki*
[
ホーム
]
一覧
最終更新
バックアップ
ヘルプ
Top
>
Dugundji compact
>
複製
?
ms
Dugundji compact をテンプレートにして作成
これらのキーワードがハイライトされています:
開始行:
*Definition [#t3351c10]
-a compact space X is Dugundji if it has one of the following equivalent properties:
++ if Z is a zero-dimensional compact space and A is a closed subset of Z, then
every continuous map A → X extends to a continuous map Z → X;
++ there exists a family Φ of closed equivalence relations on X such that:
+++ for every &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20R%5cin%5cPhi%20%5c%5d%7d%25.png); the quotient space X/R is metrizable and the quotient map X → X/R is open;
+++ ∩Φ = the diagonal of X^2 (in other words, the family Φ separates points of X);
+++ Φ is closed under countable intersections.
*Property [#g1f8d6e9]
-For every topological group X every compact G_δ-subset of X is Dugundji.
-For every [[Mul’tsetv space]] X every compact G_δ-subspace of X is Dugundji.
*Reference [#y8d40af8]
-Reznichenko, E. A.(RS-MOSCM-GT) and Uspenskij, V. V.(RS-MOSCM-GT), ''Pseudocompact Malʹtsev spaces. (English summary) '',Special issue on topological groups. ,Topology Appl. 86 (1998), no. 1, 83--104.
終了行:
*Definition [#t3351c10]
-a compact space X is Dugundji if it has one of the following equivalent properties:
++ if Z is a zero-dimensional compact space and A is a closed subset of Z, then
every continuous map A → X extends to a continuous map Z → X;
++ there exists a family Φ of closed equivalence relations on X such that:
+++ for every &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20R%5cin%5cPhi%20%5c%5d%7d%25.png); the quotient space X/R is metrizable and the quotient map X → X/R is open;
+++ ∩Φ = the diagonal of X^2 (in other words, the family Φ separates points of X);
+++ Φ is closed under countable intersections.
*Property [#g1f8d6e9]
-For every topological group X every compact G_δ-subset of X is Dugundji.
-For every [[Mul’tsetv space]] X every compact G_δ-subspace of X is Dugundji.
*Reference [#y8d40af8]
-Reznichenko, E. A.(RS-MOSCM-GT) and Uspenskij, V. V.(RS-MOSCM-GT), ''Pseudocompact Malʹtsev spaces. (English summary) '',Special issue on topological groups. ,Topology Appl. 86 (1998), no. 1, 83--104.
ページ名: