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.

The families of right (left) translation finite subsets of a discrete infinite group Γ are defined and shown to be ideals. Their kernels ZR and ZL are identified as the closure of the set of products pq (p · q) in the Čech-Stone compactification βΓ. Consequently it is shown that the map π : βΓ → Γ , the canonical semigroup homomorphism from βΓ onto Γ , the universal semitopological semigroup co...

Let β G X denote the maximal equivariant compactiίication (G-com-pactίfication) of the G-space X (i.e. a topological space X, completely regular and Hausdorff, on which the topological group G acts as a continuous transformation group). If G is locally compact and locally connected, then we show that β G (XX Y) = β G X X β G Y if and only if X X Y is what we call G-pseudocompact, provided X and...

We prove the existence of (2 , τ)-matrix points among uniform and regular points of Čech–Stone compactification of uncountable discrete spaces and discuss some properties of these points.

We prove that every compact space X is a Čech-Stone compactification of a normal subspace of cardinality at most d(X)t(X), and some facts about cardinal invariants of compact spaces.

In this study, the authors present an approach for the construction of a Stone–Céch type compactification of plain ditopological texture spaces in terms of difunctions. Mathematics Subject Classification: 54E55

The countably-compactification of a topological space X is such its extension Y, that Y completely regular and countably-compact space, any closed subset in Y. But this does not always exist. Due to this, the concept saturation appeared, which generalisation countably-compactification: instead condition countably-compactness it necessary infinite has limit point Meanwhile, second remains unchan...