‎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 ...

‎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 ...

This paper reviews the one-to-one correspondence between stably compact spaces (a topological concept covering most classes of semantic domains) and compact ordered Hausdorff spaces. The correspondence is extended to certain classes of real-valued functions on these spaces. This is the basis for transferring methods and results from functional analysis to the non-Hausdorff setting. As an applic...

The probability measures on compact Hausdorff spaces K form a compact convex subset PK of the space of measures with the vague topology. Every continuous map f : K → L of compact Hausdorff spaces induces a continuous affine map Pf : PK → PL extending P. Together with the canonical embedding ε : K → PK associating to every point its Dirac measure and the barycentric map β associating to every pr...

The compact Hausdorff space X has the Complex Stone-Weierstrass Property (CSWP) iff it satisfies the complex version of the Stone-Weierstrass Theorem. W. Rudin showed that all scattered spaces have the CSWP. We describe some techniques for proving that certain non-scattered spaces have the CSWP. In particular, if X is the product of a compact ordered space and a compact scattered space, then X ...

In this article we introduce the concept of $z^circ$-filter on a topological space $X$. We study and investigate the behavior of $z^circ$-filters and compare them  with corresponding ideals, namely, $z^circ$-ideals of $C(X)$,  the ring of real-valued continuous functions on a completely regular Hausdorff space $X$. It is observed that $X$ is a compact space if and only if every $z^circ$-filter ...

‎In this note‎, ‎we consider the concentration function problem for a continuous action of a locally compact group $G$ on a locally compact Hausdorff space $X$‎. ‎We prove a necessary and sufficient condition for the concentration functions of a‎ ‎spread-out irreducible probability measure $mu$ on $G$ to converge to zero.

It is proved that if A is aregular uniform algebra on a compact Hausdorff space X in which every closed ideal is an M-ideal, then A = C(X).

This paper is a continuation of the paper [4]. In [4] it was shown that there exists a duality Ψa between the category DSkeLC (introduced there) and the category SkeLC of locally compact Hausdorff spaces and continuous skeletal maps. We describe here the subcategories of the category DSkeLC which are dually equivalent to the following eight categories: all of them have as objects the locally co...