We study maximal pseudocompact spaces calling them also MP-spaces. We show that the product of a maximal pseudocompact space and a countable compact space is maximal pseudocompact. If X is hereditarily maximal pseudocompact then X × Y is hereditarily maximal pseudocompact for any first countable compact space Y. It turns out that hereditary maximal pseudocompactness coincides with the Preiss-Simon property in countably compact spaces. In compact spaces, hereditary MP-property is invariant under...

Topological linear spaces having the property that some sequentially continuous linear maps on them are continuous, are investigated. It is shown that such properties (and close ones, e.g., bornological-like properties) are closed under large products.

A topological space $X$ is said to be $e$-separable if $X$ has a $\sigma$-closed-discrete dense subset. Recently, G. Gruenhage and D. Lutzer showed that $e$-separable PIGO spaces are perfect and asked if $e$-separable monotonically normal spaces are perfect in general. The main purpose of this article is to provide examples of $e$-separable monotonically normal spaces which are not perfect. Extremely normal $e$-separable spaces are shown to be stratifiable.

Strongly sequential spaces were introduced and studied to solve a problem of Tanaka concerning the product of sequential topologies. In this paper, further properties of strongly sequential spaces are investigated.

It is proved that the product of two pseudo radial compact spaces is pseudo radial provided that one of them is monolithic.

We study closed subspaces of $\kappa$-Ohio complete spaces and, for $\kappa$ uncountable cardinal, we prove a characterization for them. We then investigate the behaviour of products of $\kappa$-Ohio complete spaces. We prove that, if the cardinal ${\kappa }^{+}$ is endowed with either the order or the discrete topology, the space ${\left({\kappa }^{+}\right)}^{{\kappa }^{+}}$ is not $\kappa$-Ohio complete. As a consequence, we show that, if $\kappa$ is less than the first weakly inaccessible cardinal, then neither the space ${\omega }^{{\kappa }^{+}}$, nor the space ${ℝ}^{{\kappa }^{+}}$ is $\kappa$-Ohio complete.