Existence of Semiregular Topological Space which is not Urysohn Space
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Theorem
There exists at least one example of a semiregular topological space which is not a Urysohn space.
Proof
Let $T$ be an Arens square.
From Arens Square is Semiregular, $T$ is a semiregular space.
From Arens Square is not Urysohn Space, $T$ is not a Urysohn space.
Hence the result.
$\blacksquare$
Sources
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $2$: Separation Axioms: Additional Separation Properties