## Proof That a totally Disconnected Space is Hausdorff

Theorem

A totally disconnected spaceis Hausdorff.

Proof

Letbe totally disconnected and let

Sinceis totally disconnected, disjoint open setsexist such thatand

Henceis Hausdorff.

Theorem

A totally disconnected spaceis Hausdorff.

Proof

Letbe totally disconnected and let

Sinceis totally disconnected, disjoint open setsexist such thatand

Henceis Hausdorff.