Let be a topological space. A collection of open subsets of is said to be an open cover for if .
A sub-collection of an open cover which is itself an open cover is called a sub-cover.
A topological space is said to be a Lindelof space if every open cover of has a countable sub-cover.
• A closed sub-space of a Lindelof space is Lindelof.
• Every second countable space is a Lindelof space.
Let be a second countable space. If a non-empty open set in is represented as the union of a collection of open sets, then can be represented as a countable union of .