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 space
is normal if, given any two disjoint subsets
and
of
there are disjoint open sets
and
such that
and
The indiscrete topology
consists of sets
and
Hence the only closed sets areand
because
and
Hence there are no non empty disjoint closed subsets ofThe space is normal.