Proof That Any Topological Space With the Indiscrete Topology Containing More Than One Point is Normal

Theorem

Any Topological Space With the Indiscrete Topology Containing More Than One Point is Normal

Proof

Any topological space with the indiscrete topology containing more than one point is normal

Proof

A topological spaceis normal if, given any two disjoint subsetsandof there are disjoint open setsandsuch thatand

The indiscrete topologyconsists of setsand

Hence the only closed sets areandbecauseand

Hence there are no non empty disjoint closed subsets ofThe space is normal.