Space Suggestion: Product of first uncountable ordinal with successor of the first uncountable ordinal

[Moniker1998]

Space Suggestion

Let $X$ be $\omega_1\times (\omega_1+1)$.

Rationale

This space is a classic example of a non-normal product, see e.g. Handbook of set theoretic topology chapter 18 example 2.2.

Relationship to other spaces and properties

This space provides an example satifying the search https://topology.pi-base.org/spaces?q=pseudonormal+%2B+not+normal+%2B+tychonoff

[prabau]

That is a nice classic example. For some reason I thought it would have been there already, but clearly not.