A pseudocompact group which is not strongly pseudocompact

A Pseudocompact Completely Regular Frame which is not Spatial

Compact regular frames are always spatial. In this note we present a method for constructing non-spatial frames. As an application we show that there is a countably compact (and hence pseudocompact) completely regular frame which is not spatial.

Pseudocompact Spaces

Imposing pseudocompact group topologies on Abelian groups

The least cardinal λ such that some (equivalently: every) compact group with weight α admits a dense, pseudocompact subgroup of cardinality λ is denoted by m(α). Clearly, m(α) ≤ 2. We show: Theorem 3.3. Among groups of cardinality γ, the group ⊕γQ serves as a “test space” for the availability of a pseudocompact group topology in this sense: If m(α) ≤ γ ≤ 2 then ⊕γQ admits a (necessarily connect...

Every crowded pseudocompact ccc space is resolvable

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.

Pseudocompact Totally Dense Subgroups

It was shown by Dikranjan and Shakhmatov in 1992 that if a compact abelian group K admits a proper totally dense pseudocompact subgroup, then K cannot have a torsion closed Gδ-subgroup; moreover this condition was shown to be also sufficient under LH. We prove in ZFC that this condition actually ensures the existence of a proper totally dense subgroup H of K that contains an ω-bounded dense sub...