The approximation and extension of uniformly continuous Banach space valued mappings
The Baire Set Fixing Property and Uniform Continuity in Topological Groups.
The category of uniform frames
The category of uniform spaces as a completion of the category of metric spaces
A criterion for the existence of an initial completion of a concrete category universal w.r.tḟinite products and subobjects is presented. For metric spaces and uniformly continuous maps this completion is the category of uniform spaces.
The commuting of coreflectors in uniform spaces with completion
The completion monad and its algebra
The complexity of -discretely decomposable families in uniform spaces
The convergence space of minimal usco mappings
A convergence structure generalizing the order convergence structure on the set of Hausdorff continuous interval functions is defined on the set of minimal usco maps. The properties of the obtained convergence space are investigated and essential links with the pointwise convergence and the order convergence are revealed. The convergence structure can be extended to a uniform convergence structure so that the convergence space is complete. The important issue of the denseness of the subset of all...
The coregular property on -spaces
The dimension of metrizable subspaces of Eberlein compacta and Eberlein compactifications of metrizable spaces
We prove that every Baire subspace Y of c₀(Γ) has a dense metrizable subspace X with dim X ≤ dim Y. We also prove that the Kimura-Morishita Eberlein compactifications of metrizable spaces preserve large inductive dimension. The proofs rely on new and old results concerning the dimension of uniform spaces.
The Doitchinov Completion of a Regular Paratopological Group
In memory of Professor D. Doitchinov ∗ This paper was written while the first author was supported by the Swiss National Science Foundation under grants 21–30585.91 and 2000-041745.94/1 and by the Spanish Ministry of Education and Sciences under DGES grant SAB94-0120. The second author was supported under DGES grant PB95-0737. During her stay at the University of Berne the third author was supported by the first author’s grant 2000-041745.94/1 from the Swiss National Science Foundation.We show...
The Dugundji extension property can fail in ωµ -metrizable spaces
We show that there exist -metrizable spaces which do not have the Dugundji extension property ( with the countable box topology is such a space). This answers a question posed by the second author in 1972, and shows that certain results of van Douwen and Borges are false.
The regularity series of a Cauchy space.
The shape theory for uniform spaces and the shape uniform invariants
Three technical tools in uniform spaces
Topological contraction principle
Topological convergence and uniform convergence
Totally bounded frame quasi-uniformities
This paper considers totally bounded quasi-uniformities and quasi-proximities for frames and shows that for a given quasi-proximity on a frame there is a totally bounded quasi-uniformity on that is the coarsest quasi-uniformity, and the only totally bounded quasi-uniformity, that determines . The constructions due to B. Banaschewski and A. Pultr of the Cauchy spectrum and the compactification of a uniform frame are meaningful for quasi-uniform frames. If is a totally bounded quasi-uniformity...
Transitivity in uniform approach theory.
Two examples of reflections