Lebesgue Relators.
Lengths on semigroups and groups.
Les espaces topologiques, les espaces de proximité et les espaces uniformes d'un point de vue général
Level sets of uniform quotient mappings from Rn to R do not need to be locally connected.
We give an example of a uniform quotient map from R2 to R which has non-locally connected level sets.
Localization for Hausdorff uniform bundles.
Localization In Bundles Of Metric Spaces,
Localization in Bundles of uniform spaces
Localization with change of the base space in uniform bundles and sheaves.
Locally fine means subfine
Locally fine uniformities and normal covers
Maps and inverse systems of metric spaces
Measurable uniform spaces
Measure-Theoretic Characterizations of Certain Topological Properties
It is shown that Čech completeness, ultracompleteness and local compactness can be defined by demanding that certain equivalences hold between certain classes of Baire measures or by demanding that certain classes of Baire measures have non-empty support. This shows that these three topological properties are measurable, similarly to the classical examples of compact spaces, pseudo-compact spaces and realcompact spaces.
Mesures uniformes maximales
Metric-fine, proximally fine, and locally fine uniform spaces
Metric-fine uniform frames
A locallic version of Hager’s metric-fine spaces is presented. A general definition of -fineness is given and various special cases are considered, notably all metric frames, complete metric frames. Their interactions with each other, quotients, separability, completion and other topological properties are discussed.
Moscow spaces, Pestov-Tkačenko Problem, and -embeddings
We show that there exists an Abelian topological group such that the operations in cannot be extended to the Dieudonné completion of the space in such a way that becomes a topological subgroup of the topological group . This provides a complete answer to a question of V.G. Pestov and M.G. Tkačenko, dating back to 1985. We also identify new large classes of topological groups for which such an extension is possible. The technique developed also allows to find many new solutions to the...
Nearness and uniform type structures
Non Archimedean metric induced fuzzy uniform spaces.