Planar rational compacta and universality
We prove that in some families of planar rational compacta there are no universal elements.
Point character of uniformities and completeness
Pointless uniformities. I. Complete regularity
Pointless uniformities. II: (Dia)metrization
Points with maximal Birkhoff average oscillation
Let be a continuous map with the specification property on a compact metric space . We introduce the notion of the maximal Birkhoff average oscillation, which is the “worst” divergence point for Birkhoff average. By constructing a kind of dynamical Moran subset, we prove that the set of points having maximal Birkhoff average oscillation is residual if it is not empty. As applications, we present the corresponding results for the Birkhoff averages for continuous functions on a repeller and locally...
Pointwise compact sets of functions
Polishness of weak topologies generated by gap and excess functionals.
Porosity and compacta with dense ambiguous loci of metric projections
Positive definite functions and coincidences
Precompact contraction of metric uniformities, and the continuity of
Precompactness and total boundedness in products of metric spaces.
Précompactologies et structures uniformes
Préimages d’espaces héréditairement de Baire
The main result is slightly more general than the following statement: Let f: X → Y be a quasi-perfect mapping, where X is a regular space and Y a Hausdorff totally non-meagre space; if X or Y is χ-scattered, or if Y is a Lasnev space, then X is totally non-meagre. In particular, the product of a compact space X and a Hausdorff regular totally non-meagre space Y which is χ-scattered or a Lasnev space, is totally non-meagre.
Preimages of Baire spaces
A simple machinery is developed for the preservation of Baire spaces under preimages. Subsequently, some properties of maps which preserve nowhere dense sets are given.
Prescribed ultrametrics
Preservation of the Borel class under open-LC functions
Let X be a Borel subset of the Cantor set C of additive or multiplicative class α, and f: X → Y be a continuous function onto Y ⊂ C with compact preimages of points. If the image f(U) of every clopen set U is the intersection of an open and a closed set, then Y is a Borel set of the same class α. This result generalizes similar results for open and closed functions.
Prime extensions and nearness structures
Probabilistic approach spaces
We study a probabilistic generalization of Lowen's approach spaces. Such a probabilistic approach space is defined in terms of a probabilistic distance which assigns to a point and a subset a distance distribution function. We give a suitable axiom scheme and show that the resulting category is isomorphic to the category of left-continuous probabilistic topological convergence spaces and hence is a topological category. We further show that the category of Lowen's approach spaces is isomorphic to...
Probabilistic convergence spaces and generalized metric spaces.
Probabilistic convergence spaces and regularity.