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 show that the tangle space of a graph, which compactifies it, is quotient its Stone-Čech remainder obtained by contracting connected components.

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.

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