View source for Locally finite family

''of sets in a topological space''

A family <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/l/l060/l060400/l0604001.png" /> of sets such that every point of the space has a neighbourhood that intersects only finitely many elements of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/l/l060/l060400/l0604002.png" />. Locally finite families of open sets and locally finite open coverings are important. Thus, a [[Regular space|regular space]] is metrizable if and only if has a base that splits into countably many locally finite families. Any open covering of a [[Metric space|metric space]] can be refined to a locally finite open covering. Spaces that have this property are called paracompact (cf. [[Paracompact space|Paracompact space]]).



====Comments====
See also [[Locally finite covering|Locally finite covering]].