Pseudocompact spaces and functionally determined uniformities

Pseudocompact Spaces

Maximal pseudocompact spaces

Maximal pseudocompact spaces (i.e. pseudocompact spaces possessing no strictly stronger pseudocompact topology) are characterized. It is shown that submaximal pseudocompact spaces whose pseudocompact subspaces are closed need not be maximal pseudocompact. Various techniques for constructing maximal pseudocompact spaces are described. Maximal pseudocompactness is compared to maximal feeble compa...

Uniformities in fuzzy metric spaces

The aim of this paper is to study induced (quasi-)uniformities in Kramosil and Michalek's fuzzy metric spaces. Firstly, $I$-uniformity in the sense of J. Guti'{e}rrez  Garc'{i}a and $I$-neighborhood system in the sense of H"{o}hle and u{S}ostak are induced by the given fuzzy metric. It is shown that the fuzzy metric and the induced $I$-uniformity will generate the same $I$-neighborhood system. ...

Spaces Whose Pseudocompact Subspaces Are Closed Subsets

Every first countable pseudocompact Tychonoff space X has the property that every pseudocompact subspace of X is a closed subset of X (denoted herein by “FCC”). We study the property FCC and several closely related ones, and focus on the behavior of extension and other spaces which have one or more of these properties. Characterization, embedding and product theorems are obtained, and some exam...

Quasi Uniformities: Reconciling Domains with Metric Spaces

We show that quasi-metric or quasi-uniform spaces provide, inter alia, a common generalization of cpo's and metric spaces as used in denotational semantics. To accommodate the examples suggested by computer science, a reworking of basic notions involving limits and completeness is found to be necessary. Specific results include general fixed point theorem and a sequential completion construction.