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
>
coparacompact
>
複製
?
ms
coparacompact 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 [#b3ca886d]
A Hausdorff space X is called equi-locally convex (ELCX) if there exists an open neighborhood U of the diagonal &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$%5cDelta%5csubset%20X%5ctimes%20X$%7d%25.png);, a mapping &ref(ht
++for any t in I and x in X, &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$%5cvarphi%28x%2cx%2ct%29=x$%7d%25.png);;
++for any x,y in X, &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$%5cvarphi%28x%2cy%2c0%29=x$%7d%25.png); and &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$%5cvarphi%28x%2cy%2c1%29=y$%7d%25.png);;
++for any &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$V_%5calpha%20%5cin%20%5cmathcal%7bV%7d$%7d%25.png);, &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$V_%5calpha%20%5ctimes%20V_%5calpha%20%5csubset%20U$
++for any &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$V_%5calpha%20%5cin%20%5cmathcal%7bV%7d$%7d%25.png);, &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$%5cvarphi%28V_%5calpha%20%5ctimes%20V_%5calpha%20%5
A subset W in X is called convex if &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$W%5ctimes%20W%5csubset%20U$%7d%25.png); and &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$%5cvarphi%28W%5ctimes%20W%5ctimes%
The cover &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$%5cmathcal%7bV%7d$%7d%25.png); is called a convex open cover of X.
An ELCX space is called coparacompact if any open cover has a [[locally finite]] convex refinement.
*Reference [#o22497c6]
Vladimir P. Okhezin, ''On the fixed-point theory for non-compact maps and spaces.I'', Topological Methods in Nonlinear Analysis, Journal of the Juliusz Schauder Center, Volume 5, 1995, 83-100.
終了行:
*Definition [#b3ca886d]
A Hausdorff space X is called equi-locally convex (ELCX) if there exists an open neighborhood U of the diagonal &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$%5cDelta%5csubset%20X%5ctimes%20X$%7d%25.png);, a mapping &ref(ht
++for any t in I and x in X, &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$%5cvarphi%28x%2cx%2ct%29=x$%7d%25.png);;
++for any x,y in X, &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$%5cvarphi%28x%2cy%2c0%29=x$%7d%25.png); and &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$%5cvarphi%28x%2cy%2c1%29=y$%7d%25.png);;
++for any &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$V_%5calpha%20%5cin%20%5cmathcal%7bV%7d$%7d%25.png);, &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$V_%5calpha%20%5ctimes%20V_%5calpha%20%5csubset%20U$
++for any &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$V_%5calpha%20%5cin%20%5cmathcal%7bV%7d$%7d%25.png);, &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$%5cvarphi%28V_%5calpha%20%5ctimes%20V_%5calpha%20%5
A subset W in X is called convex if &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$W%5ctimes%20W%5csubset%20U$%7d%25.png); and &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$%5cvarphi%28W%5ctimes%20W%5ctimes%
The cover &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$%5cmathcal%7bV%7d$%7d%25.png); is called a convex open cover of X.
An ELCX space is called coparacompact if any open cover has a [[locally finite]] convex refinement.
*Reference [#o22497c6]
Vladimir P. Okhezin, ''On the fixed-point theory for non-compact maps and spaces.I'', Topological Methods in Nonlinear Analysis, Journal of the Juliusz Schauder Center, Volume 5, 1995, 83-100.
ページ名: