Regular $G_{\delta }$-diagonals and some upper bounds for cardinality of topological spaces

Ivan S. Gotchev, Mikhail G. Tkachenko, Vladimir V. Tkachuk

We prove that, under CH, any space with a regular $G_{\delta }$-diagonal and caliber ${\omega }_1$ is separable; a corollary of this result answers, under CH, a question of Buzyakova. For any Urys…