locally finite collection

Let $\mathcal{C}$ be a collection of subsets of a topological space $X$.

$\mathcal{C}$ is said to be locally finite if for all $x\in X$ there is a neighbourhood $U$ of $x$ such that $U\cap A=\varnothing$ for all but finitely many $A\in\mathcal{C}$.

Similarly, $\mathcal{C}$ is said to be locally countable if for all $x\in X$ there is a neighbourhood $U$ of $x$ such that $U\cap A=\varnothing$ for all but countably many $A\in\mathcal{C}$.

Title locally finite collection LocallyFiniteCollection 2013-03-22 12:12:51 2013-03-22 12:12:51 yark (2760) yark (2760) 11 yark (2760) Definition msc 54D20 PointFinite locally finite locally countable collection locally countable