On cardinality bounds for homogeneous spaces and the Gκ-modification of a space

On the cardinality of n-Urysohn and n-Hausdorff spaces

“…Theorem 3.7. [11] If X is an n-Hausdorff homogeneous space, with n ≥ 2, then |X| ≤ d(X) πχ(X) . Also recall that a space is quasiregular if every nonempty open set contains a nonempty regular closed set.…”