When is a space Lindelöf?

Question

Topological space is Lindelöf if every of its open covers has a countable one. Or equivalently every system of closed elements with countable intersection property has non empty intersection.

There exists a characterization for metric spaces: Metric space is Lindelöf if and only if it is separable or (and) second-countable.

Are there any other interesting characterizations or sufficient conditions for a space to be Lindelöf?

Answer 1

Closed subspace of Lindelöf space is Lindelöf. Two product spaces one of them compact and others Lindelöf is Lindelöf. If the space has countable basis is Lindelöf.