We prove that hereditarily disconnected countably compact groups are zero-dimensional. This gives a strongly positive answer to a question of Shakhmatov. We show that hereditary or total disconnectedness yields zerodimensionality in various classes of pseudocompact groups.

Let G be any Hausdorff topological group and let βGX denote the maximal G-compactification of a G-Tychonoff space X (i.e., a Tychonoff G-space possessing a G-compactification). Recall that a completely regular Hausdorff topological space is called pseudocompact if every continuous function f : X →R is bounded. In this paper, we prove that if X and Y are two G-Tychonoff spaces such that the prod...

P is the class of pseudocompact Hausdorff topological groups, and P′ is the class of groups which admit a topology T such that (G,T ) ∈ P. It is known that every G= (G,T ) ∈ P is totally bounded, so for G ∈ P′ the supremum T ∨(G) of all pseudocompact group topologies on G and the supremum T #(G) of all totally bounded group topologies on G satisfy T ∨ ⊆ T #. The authors conjecture for abelian G...

We prove that every pseudocompact crowed ccc space is c-resolvable. This gives a partial answer to problems posed by Comfort and Garćıa-Ferriera, and Juhász, Soukup and Szentmiklóssy.

For every natural number n, any continuous function on the product of X1×X2×...×Xn pseudocompact spaces extends to a separately βX1×βX2×...×βXn their Stone-Cech compactifications.

Every first countable pseudocompact Tychonoff space X has the property that every pseudocompact subspace of X is a closed subset of X (denoted herein by “FCC”). We study the property FCC and several closely related ones, and focus on the behavior of extension and other spaces which have one or more of these properties. Characterization, embedding and product theorems are obtained, and some exam...

We define $\Delta$-Baire spaces. If a paratopological group $G$ is space, then topological group. Locally pseudocompact spaces, Baire $p$-spaces, $\Sigma$-spaces, products of \v{C}ech-complete spaces are