Namespaces
Variants
Actions

Difference between revisions of "Lindelöf space"

From Encyclopedia of Mathematics
Jump to: navigation, search
(Importing text file)
 
m (moved Lindelöf space to Lindelof space: ascii title)
(No difference)

Revision as of 18:53, 24 March 2012

finally-compact space

A topological space 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 of a Lindelöf space into a topological space, the subspace 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: http://encyclopediaofmath.org/index.php?title=Lindel%C3%B6f_space&oldid=12592
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article