Indiscrete Space is T4
Jump to navigation
Jump to search
Theorem
Let $T = \struct {S, \set {\O, S} }$ be an indiscrete topological space.
Then $T$ is a $T_4$ space.
Proof
We have that an indiscrete space is a $T_5$ space.
Then we have that a $T_5$ Space is a $T_4$ Space.
$\blacksquare$
Sources
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text {II}$: Counterexamples: $4$. Indiscrete Topology: $10$