Universal spaces for locally finite-dimensional and strongly countable-dimensional metrizable spaces
Universal spaces in the theory of transfinite dimension, I
R. Pol has shown that for every countable ordinal α, there exists a universal space for separable metrizable spaces X with ind X = α . We prove that for every countable limit ordinal λ, there is no universal space for separable metrizable spaces X with Ind X = λ. This implies that there is no universal space for compact metrizable spaces X with Ind X = λ. We also prove that there is no universal space for compact metrizable spaces X with ind X = λ.
Universal spaces in the theory of transfinite dimension, II
We construct a family of spaces with “nice” structure which is universal in the class of all compact metrizable spaces of large transfinite dimension , or, equivalently, of small transfinite dimension ; that is, the family consists of compact metrizable spaces whose transfinite dimension is , and every compact metrizable space with transfinite dimension is embeddable in a space of the family. We show that the least possible cardinality of such a universal family is equal to the least possible...
Universalité forte pour les sous-ensembles totalement bornés. Applications aux espaces
Universality of the μ-predictor
For suitable topological spaces X and Y, given a continuous function f:X → Y and a point x ∈ X, one can determine the value of f(x) from the values of f on a deleted neighborhood of x by taking the limit of f. If f is not required to be continuous, it is impossible to determine f(x) from this information (provided |Y| ≥ 2), but as the author and Alan Taylor showed in 2009, there is nevertheless a means of guessing f(x), called the μ-predictor, that will be correct except on a small set; specifically,...
Universally image partition regularity.
Universally Kuratowski–Ulam spaces
We introduce the notions of Kuratowski-Ulam pairs of topological spaces and universally Kuratowski-Ulam space. A pair (X,Y) of topological spaces is called a Kuratowski-Ulam pair if the Kuratowski-Ulam Theorem holds in X× Y. A space Y is called a universally Kuratowski-Ulam (uK-U) space if (X,Y) is a Kuratowski-Ulam pair for every space X. Obviously, every meager in itself space is uK-U. Moreover, it is known that every space with a countable π-basis is uK-U. We prove the following: ...
Universalmengen bezüglich der Lage im
Un’osservazione su una sottoalgebra di
Un'osservazione sugli autoomeomorfismi dei cerchi
Unraveling the Tangled Complexity of DNA: Combining Mathematical Modeling and Experimental Biology to Understand Replication, Recombination and Repair
How does DNA, the molecule containing genetic information, change its three-dimensional shape during the complex cellular processes of replication, recombination and repair? This is one of the core questions in molecular biology which cannot be answered without help from mathematical modeling. Basic concepts of topology and geometry can be introduced in undergraduate teaching to help students understand counterintuitive complex structural transformations...
Upper and Lower Bounds in Relator Spaces
2000 Mathematics Subject Classification: 06A06, 54E15An ordered pair X(R) = ( X, R ) consisting of a nonvoid set X and a nonvoid family R of binary relations on X is called a relator space. Relator spaces are straightforward generalizations not only of uniform spaces, but also of ordered sets. Therefore, in a relator space we can naturally define not only some topological notions, but also some order theoretic ones. It turns out that these two, apparently quite different, types of notions are closely...
Upper quasi continuous maps and quasi continuous selections
The paper deals with the existence of a quasi continuous selection of a multifunction for which upper inverse image of any open set with compact complement contains a set of the form , where is open and , are from a given ideal. The methods are based on the properties of a minimal multifunction which is generated by a cluster process with respect to a system of subsets of the form .
Upper semicontinuity of automorphism groups.
Upper semicontinuous decompositions of convex metric spaces
Upper semicontinuous decompositions of spaces having bases of countable order
Urysohn universal spaces as metric groups of exponent 2
The aim of the paper is to prove that the bounded and unbounded Urysohn universal spaces have unique (up to isometric isomorphism) structures of metric groups of exponent 2. An algebraic-geometric characterization of Boolean Urysohn spaces (i.e. metric groups of exponent 2 which are metrically Urysohn spaces) is given.
Urysohn’s lemma, gluing lemma and contraction mapping theorem for fuzzy metric spaces
In this paper the concept of a fuzzy contraction mapping on a fuzzy metric space is introduced and it is proved that every fuzzy contraction mapping on a complete fuzzy metric space has a unique fixed point.
Useful properties of index pairs for upper semicontinuous multivalued dynamical systems.
Using implicit relations to prove unified fixed point theorems in metric and 2-metric spaces.