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locally_finite_topology_subset [2016/09/14 15:52]
nikolaj
locally_finite_topology_subset [2016/09/15 01:42] (current)
nikolaj
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 === Dicussion === === Dicussion ===
-  * A topologal space is //​paracompact//​ if it has a cover with that property.+  * A topologal space is //​paracompact//​ if it any cover has a refinement ​with that property.
   * The sample of $V$'s above may be very big, so ${\mathcal C}$ is really only small w.r.t. the sample. In a //compact// space, on the other hand, the cover itself is finite (and you don't need to consider that sample). ​   * The sample of $V$'s above may be very big, so ${\mathcal C}$ is really only small w.r.t. the sample. In a //compact// space, on the other hand, the cover itself is finite (and you don't need to consider that sample). ​
   * Note that the name //locally compact// is already used for the situation where every point $x\in X$ has a compact neighborhood $V$.    * Note that the name //locally compact// is already used for the situation where every point $x\in X$ has a compact neighborhood $V$. 
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