# Differences

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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 Both sides previous revision Previous revision 2016/09/15 01:42 nikolaj 2016/09/14 15:52 nikolaj 2016/09/14 15:37 nikolaj 2016/09/14 15:34 nikolaj 2016/09/14 15:31 nikolaj 2016/09/14 15:30 nikolaj 2016/09/14 15:30 nikolaj 2016/09/14 15:28 nikolaj 2016/09/14 15:16 nikolaj created 2016/09/15 01:42 nikolaj 2016/09/14 15:52 nikolaj 2016/09/14 15:37 nikolaj 2016/09/14 15:34 nikolaj 2016/09/14 15:31 nikolaj 2016/09/14 15:30 nikolaj 2016/09/14 15:30 nikolaj 2016/09/14 15:28 nikolaj 2016/09/14 15:16 nikolaj created Line 16: Line 16: === 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 $V$.