Definition:Open Locally Finite Set of Subsets

Definition

Let $T = \struct {S, \tau}$ be a topological space.

Let $\UU$ be a set of subsets of $S$.

Then $\UU$ is open locally finite if and only if:

$(1) \quad \UU \subseteq \tau$, that is, for all $U \in \UU: U$ is open in $T$

$(2) \quad \UU$ is locally finite

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