Open Cover:
            Let  be a topological space. A collection  of open subsets of  is said to be open cover for  if .
            A sub-collection of an open cover which is itself an open cover is called a sub-cover.

Lindelof Space:
            A topological space  is said to be a Lindelof space if every open cover of  has a countable sub-cover.

Theorems:

• A closed sub-space of Lindelof space is Lindelof.
• Every second countable space is Lindelof space.

Lindelof Theorem:
            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 .