On the cardinality of $S(n)$-spaces

Alexander V. Osipov

Published 2018-09-25Version 1

In this paper we continue to study of properties of $S(n)$-spaces. We establish bounded on the cardinality of $S(n)$-spaces. Also we constructed the example of $S(n)$ not $\theta^n$-Urysohn space for every $n\geq 2$. This is the answer to the question of F.A. Basile, N. Carlson and J. Porter.