A Regular Space Without a Uniformly Regular Quasi-Uniformity.
Uniform entropy vs topological entropy
We discuss the connection between the topological entropy and the uniform entropy and answer several open questions from [10, 15]. We also correct several erroneous statements given in [10, 18] without proof.
A nontransitive space based on combinatorics
Costruiamo uno spazio nontransitivo analogo al piano di Kofner. Mentre gli argomenti usati per la costruzione del piano di Kofner si fondano su riflessioni geometriche, le nostre prove si basano su idee combinatorie.
On -discrete Borel mappings via quasi-metrics
Characterizations of absolute -sets
On uniformly locally compact quasi-uniform hyperspaces
We characterize those Tychonoff quasi-uniform spaces for which the Hausdorff-Bourbaki quasi-uniformity is uniformly locally compact on the family of nonempty compact subsets of . We deduce, among other results, that the Hausdorff-Bourbaki quasi-uniformity of the locally finite quasi-uniformity of a Tychonoff space is uniformly locally compact on if and only if is paracompact and locally compact. We also introduce the notion of a co-uniformly locally compact quasi-uniform space and show...
A metrizable completely regular ordered space
We construct a completely regular ordered space such that is an -space, the topology of is metrizable and the bitopological space is pairwise regular, but not pairwise completely regular. (Here denotes the upper topology and the lower topology of .)
-fuzzy compactness in -topological spaces.
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