Academic Journal
Disconnectedness properties of hyperspaces
| العنوان: | Disconnectedness properties of hyperspaces |
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| المؤلفون: | Hernández-Gutiérrez, Rodrigo, Tamariz-Mascarúa, Angel |
| بيانات النشر: | Charles University in Prague, Faculty of Mathematics and Physics |
| سنة النشر: | 2011 |
| المجموعة: | DML-CZ (Czech Digital Mathematics Library) |
| مصطلحات موضوعية: | keyword:hyperspaces, keyword:Vietoris topology, keyword:$F'$-space, keyword:$P$-space, keyword:hereditarily disconnected, msc:54B20, msc:54G05, msc:54G10, msc:54G12, msc:54G20 |
| الوصف: | summary:Let $X$ be a Hausdorff space and let $\mathcal H$ be one of the hyperspaces $CL(X)$, $\mathcal K(X)$, $\mathcal F(X)$ or $\mathcal F_n(X)$ ($n$ a positive integer) with the Vietoris topology. We study the following disconnectedness properties for $\mathcal H$: extremal disconnectedness, being a $F'$-space, $P$-space or weak $P$-space and hereditary disconnectedness. Our main result states: if $X$ is Hausdorff and $F\subset X$ is a closed subset such that (a) both $F$ and $X-F$ are totally disconnected, (b) the quotient $X/F$ is hereditarily disconnected, then $\mathcal K(X)$ is hereditarily disconnected. We also show an example proving that this result cannot be reversed. |
| نوع الوثيقة: | text |
| وصف الملف: | application/pdf |
| اللغة: | English |
| تدمد: | 0010-2628 1213-7243 |
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| الاتاحة: | http://hdl.handle.net/10338.dmlcz/141742 |
| Rights: | access:Unrestricted ; rights:DML-CZ Czech Digital Mathematics Library, http://dml.cz/ ; rights:Institute of Mathematics AS CR, http://www.math.cas.cz/ ; conditionOfUse:http://dml.cz/use |
| رقم الانضمام: | edsbas.E0023F18 |
| قاعدة البيانات: | BASE |
| تدمد: | 00102628 12137243 |
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