Über Peano-Kurven.
Ultrametric spaces bi-Lipschitz embeddable in
It is proved that if an ultrametric space can be bi-Lipschitz embedded in , then its Assouad dimension is less than n. Together with a result of Luukkainen and Movahedi-Lankarani, where the converse was shown, this gives a characterization in terms of Assouad dimension of the ultrametric spaces which are bi-Lipschitz embeddable in .
Ultraparacompactness in certain Pixley-Roy hyperspaces
Ultrasmoothness in dendroids
The class of ultrasmooth dendroids is contained in the class of smooth dendroids and contains the class of locally connected dendroids. In this paper we study relationships between ultrasmoothness and smoothness in dendroids and we characterize ultrasmooth dendroids.
Una extensión transfinita de la dimensión por recubrimientos.
Uncountable ω-limit sets with isolated points
We give two examples of tent maps with uncountable (as it happens, post-critical) ω-limit sets, which have isolated points, with interesting structures. Such ω-limit sets must be of the form C ∪ R, where C is a Cantor set and R is a scattered set. Firstly, it is known that there is a restriction on the topological structure of countable ω-limit sets for finite-to-one maps satisfying at least some weak form of expansivity. We show that this restriction does not hold if the ω-limit set is uncountable....
Une approche non-standard de la dimension d'un espace topologique
Unicoherence in means
Unified spaces and singular sets for mappings of locally compact spaces
Uniform dimension of mappings (Preliminary communication)
Uniform sequences of -mappings
Uniformization of Topological Spaces with Small Inductive Dimension Zero.
Unique -closure for some -groups of rational valued functions
Usually, an abelian -group, even an archimedean -group, has a relatively large infinity of distinct -closures. Here, we find a reasonably large class with unique and perfectly describable -closure, the class of archimedean -groups with weak unit which are “-convex”. ( is the group of rationals.) Any is -convex and its unique -closure is the Alexandroff algebra of functions on defined from the clopen sets; this is sometimes .
Universal acyclic resolutions for arbitrary coefficient groups
We prove that for every compactum X and every integer n ≥ 2 there are a compactum Z of dimension ≤ n+1 and a surjective -map r: Z → X such that for every abelian group G and every integer k ≥ 2 such that we have and r is G-acyclic.
Universal analytic preorders arising from surjective functions
Examples are presented of Σ₁¹-universal preorders arising by requiring the existence of particular surjective functions. These are: the relation of epimorphism between countable graphs; the relation of being a continuous image (or a continuous image of some specific kind) for continua; the relation of being continuous open image for dendrites.
Universal completely regular dendrites
We define a dendrite which is universal in the class of all completely regular dendrites with order of points not greater than n. In particular, the dendrite is universal in the class of all completely regular dendrites. The construction starts with the standard universal dendrite of order n described by J. J. Charatonik.
Universal continua
Universal mappings and weakly confluent mappings
Universal maps of Cartesian products
Universal meager -sets in locally compact manifolds
In each manifold modeled on a finite or infinite dimensional cube , , we construct a meager -subset which is universal meager in the sense that for each meager subset there is a homeomorphism such that . We also prove that any two universal meager -sets in are ambiently homeomorphic.