Sierpiński Space is T4

Theorem

Let $T = \struct {\set {0, 1}, \tau_0}$ be a Sierpiński space.

Then $T$ is a $T_4$ space.


Proof

We have that the Sierpiński Space is $T_5$.

Then we have that a $T_5$ Space is $T_4$.

$\blacksquare$


Sources

  • 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text {II}$: Counterexamples: $11$. Sierpinski Space: $18$
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