Lindelöf space

A Lindelöf space is a mathematical object from the set-theoretic topology. It is a concept which generalizes the compact space. Named is the Lindelöf space after the mathematician Ernst Leonard Lindelöf.

Definition

A topological space is called a Lindelöf space if every open cover has a countable subcover.

Set of Lindelöf

Has the topological space has a countable base, so is a Lindelöf space.

Other properties

• Every compact space is a Lindelöf space.
• A topological space is compact if it is countably compact and Lindelöf space.
• For metrizable spaces, the three properties are zweitabzählbar, Lindelöf and separable equivalent.
• Closed subspaces of Lindelöf spaces are Lindelöf spaces again.