Lindelöf space

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finally-compact space

A topological space $X$ such that every open covering (cf. Covering (of a set)) of it contains a countable subcovering. For example, a space with a countable base is a Lindelöf space; every quasi-compact space is a Lindelöf space. Every closed subspace of a Lindelöf space is a Lindelöf space. For every continuous mapping $f$ of a Lindelöf space $X$ into a topological space, the subspace $f(X)$ of the latter is a Lindelöf space. Every Hausdorff space that is the union of a countable family of compact (Hausdorff) sets is a Lindelöf space. Every regular Lindelöf space is paracompact (cf. Paracompact space). The product of a Lindelöf space and a compact (Hausdorff) space is a Lindelöf space.

How to Cite This Entry:
Lindelöf space. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article