Trait Suggestion: Cohen's modified product S207 is not Connected P36

[GeoffreySangston]

Trait Suggestion

Cohen's modified product S207 is not Connected P36. Unknown today https://topology.pi-base.org/spaces/S000207/properties/P000036

Proof/References

The topology is finer than the product topology on $\omega_1 \times (\omega_1 + 1)$.

[GeoffreySangston]

I think it would be more efficient to assert Totally separated actually, for the same reason as here https://github.com/pi-base/data/issues/1040#issuecomment-2530005460, and because 'Totally separated' is preserved by making the topology finer.

Not sure if there's not a more efficient property to assert.