nLab locally finite set of subsets

Definition

Given a topological space $X$, then a set of subset $\{S_i \subset X\}_{i \in I}$ is locally finite if every point $x \in X$ has an open neighbourhood thatintersects only a finite number of the $S_i$.

Often this property is considered for open covers, see at locally finite open cover. But the condition also plays a role for collections of subsets which are not open or not covering, for instance in Michael's theorem (Michael 53, theorem 1).

Related concepts

• countably locally finite set of subsets

• countably locally discrete set of subsets

• locally finite cover

• locally finite cell complex

References

• Ernest Michael, A note on paracompact spaces, Proc. Amer. Math. Soc. 1953 (jstor, pdf)