‎It is well known that every (real or complex) normed linear space $L$ is isometrically embeddable into $C(X)$ for some compact Hausdorff space $X$‎. ‎Here $X$ is the closed unit ball of $L^*$ (the set of all continuous scalar-valued linear mappings on $L$) endowed with the weak$^*$ topology‎, ‎which is compact by the Banach--Alaoglu theorem‎. ‎We prove that the compact Hausdorff space $X$ can ...

Abstract We introduce the notion of an introverted Boolean algebra $\mathcal{B}$ closed-and-open subsets a topological group G, show that associated Stone space $(\nu_{\mathcal{B}} \nu_{\mathcal{B}})$ is totally disconnected semigroup compactification G and every takes this form. identify study universal compactification, semitopological G. Our main results are obtained independently Gelfand th...

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 that the semigroup operation of a topological semigroup S extends to a continuous semigroup operation on its the Stone-Čech compactification βS provided S is a pseudocompact openly factorizable space, which means that each map f : S → Y to a second countable space Y can be written as the composition f = g ◦ p of an open map p : X → Z onto a second countable space Z and a map g : Z → Y ...

The Stone-Cech compactification of a space X is described by adjoining to X continuous images of the Stone-tech growths of a complementary pair of subspaces of X. The compactification of an example of Potoczny from [P] is described in detail. The Stone-Cech compactification of a completely regular space X is a compact Hausdorff space ßX in which X is dense and C*-embedded, i.e. every bounded re...