Products of straight spaces with compact spaces

Products of straight spaces

A metric space X is straight if for each finite cover of X by closed sets, and for each real valued function f on X , if f is uniformly continuous on each set of the cover, then f is uniformly continuous on the whole of X . A locally connected space is straight iff it is uniformly locally connected (ULC). It is easily seen that ULC spaces are stable under finite products. On the other hand the ...

Products of Nearly Compact Spaces

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 ...

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...

On function spaces of Corson-compact spaces

We apply elementary substructures to characterize the space Cp(X) for Corsoncompact spaces. As a result, we prove that a compact space X is Corson-compact, if Cp(X) can be represented as a continuous image of a closed subspace of (Lτ ) × Z, where Z is compact and Lτ denotes the canonical Lindelöf space of cardinality τ with one non-isolated point. This answers a question of Archangelskij [2].