Some strains of Staphylococcus aureus grew as compact colonies in Brain Heart Infusion-serum-soft agar but as diffuse colonies in a modified Staphylococcus 110-serum-soft agar. These strains were designated "pseudocompact." Strains showing compact-type colonial morphology in both media were designated "compact," whereas strains showing diffuse-type growth in both media were designated "diffuse....

J. Keesling has shown that for connected spaces X the natural inclusion e : X → βX of X in its Stone-Čech compactification is a shape equivalence if and only if X is pseudocompact. This paper establishes the analogous result for strong shape. Moreover, pseudocompact spaces are characterized as spaces which admit compact resolutions, which improves a result of I. Lončar.

We define pseudocompact topological spaces and prove that every compact space is pseudocompact. We also solve an exercise from [16] p.225 that the for a topological space X the following are equivalent: • Every continuous real map from X is bounded (i.e. X is pseudocompact). • Every continuous real map from X attains minimum. • Every continuous real map from X attains maximum. Finally, for a co...

We show that all Ψ-spaces associated to maximal almost disjoint families have pseudocompact Vietoris hyperspace if and only MAc(P(ω)/fin) holds. further study the question whether there is a family whose construct consistent example of size ω2<c not pseudocompact.

We study the natural inclusions of Cb(X)⊗A into Cb(X,A) and Cb ( X,Cb(Y ) ) into Cb(X × Y ). In particular, excepting trivial cases, both these maps are isomorphisms only when X and Y are pseudocompact. This implies a result of Glicksberg showing that the Stone-Čech compactificiation β(X × Y ) is naturally identified with βX × βY if and only if X and Y are pseudocompact.

A topological group is locally pseudocompact if it contains a non-empty open set with pseudocompact closure. In this note, we study connectedness and disconnectedness properties of groups G with the property that every closed subgroup of G is locally pseudocompact. We show that the completion of the component G0 of G contains every connected compact subgroup of the completion of G. We also prov...

S. Garćıa-Ferreira and H. Ohta gave a construction that was intended to produce a τ -pseudocompact space, which has a regular-closed zero set A and a regular-closed C-embedded set B such that neither A nor B is τ pseudocompact. We show that although their sets A, B are not regular-closed, there are at least two ways to make their construction work to give the desired example.

We investigate the question: which compact abelian groups have a dense (pseudocompact) subgroup without convergent sequences?