Excluded Point Topology is not T3
Jump to navigation
Jump to search
Theorem
Let $T = \struct {S, \tau_{\bar p} }$ be a excluded point space.
Then $T$ is not a $T_3$ space.
Proof
- Excluded Point Topology is Open Extension Topology of Discrete Topology
- Open Extension Topology is not T3
$\blacksquare$
Sources
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text {II}$: Counterexamples: $13 \text { - } 15$. Excluded Point Topology: $2$