Proof That Every closed Subspace of a Lindelof Space is a Lindelof Space
Every closed subspace of a Lindelof space is a Lindelof space.
Supposeis a closed subspace of a Lindelof spaceandis an open cover ofEachfor someopen in
Sinceis closed,is open inhenceis an open cover of
There is a countable subcoversois a countable cover of
Henceis a countable open subcover ofandis a Lindelof space.