A connected pseudocompact space

Concerning Connected, Pseudocompact Abelian Groups

It is known that if P is either the property w-bounded or countably compact, then for every cardinal a 2 w there is a P-group G such that H.G = a and no proper, dense subgroup of G is a P-group. What happens when P is the property pseudocompact? The first-listed author and Robertson have shown that every zero-dimensional Abelian P-group G with H.G > o has a proper, dense, P-group. Turning to th...

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 Spaces

Attribute-Space Connected Filters

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...