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locally_finite_topology_subset [2016/09/14 15:34] nikolaj |
locally_finite_topology_subset [2016/09/14 15:37] nikolaj |
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| === Idea === | === Idea === | ||
| - | Like many properties, this is a notion of smallness. It's not about the smallness of a subset $U$ of $X$, but smallness of a collection ${\mathcal C}$ of subsets $U$ of $X$. | + | Like many properties, this is a notion of smallness. It's not about the smallness of a subset $U$ of $X$, but smallness of a collection ${\mathcal C}$ of subsets $U$ of $X$. |
| - | You may consider a well choosen collection of neighborhoods (the sets $V\in{\mathcal T}$) and ${\mathcal C}$ ought to be countable w.r.t. to that sample, i.e. pro $V$. | + | You may consider a well choosen sample of neighborhoods (the sets $V\in{\mathcal T}$) and ${\mathcal C}$ ought to be finite with respect to that sample (countable //pro// $V$). |
| === Dicussion === | === Dicussion === | ||
