Products of sequential CLP-compact spaces are CLP-compact

Products of sequential CLP-compact spaces are CLP-compact

It is shown that the product of finitely many sequential, CLP-compact spaces is CLPcompact. The class of spaces which have the property that every cover by clopen sets — sets which are both open and closed — has a finite subcover was introduced by A. Šostak in [1] under the name CBcompact. These spaces are now known as CLP-compact spaces and their study is linked to the question of whether the ...

Products of Nearly Compact Spaces

Imagining Clp(, ) Imagining Clp(, )

We study under which conditions the domain of-terms (() and the equality theory of the-calculus () form the basis of a usable constraint logic programming language (CLP). The conditions are that the equality theory must contain axiom , and the formula language must depart from Horn clauses and accept universal quantiications and implications in goals. In short, CLP((,) must be close to Prolog. ...

Compact Factors in Finally Compact Products of Topological Spaces

We present instances of the following phenomenon: if a product of topological spaces satisfies some given compactness property then the factors satisfy a stronger compactness property, except possibly for a small number of factors. The first known result of this kind, a consequence of a theorem by A. H. Stone, asserts that if a product is regular and Lindelöf then all but at most countably many...

Compact Metrizable Groups Are Isometry Groups of Compact Metric Spaces

This note is devoted to proving the following result: given a compact metrizable group G, there is a compact metric space K such that G is isomorphic (as a topological group) to the isometry group of K.