A fixed point theorem for non-expansive mappings on compact metric spaces.
A formal analogy between proximity and finite dimensionality
A Galois connection between distance functions and inequality relations
Following the ideas of R. DeMarr, we establish a Galois connection between distance functions on a set and inequality relations on . Moreover, we also investigate a relationship between the functions of and .
A game and its relation to netweight and D-spaces
We introduce a two player topological game and study the relationship of the existence of winning strategies to base properties and covering properties of the underlying space. The existence of a winning strategy for one of the players is conjectured to be equivalent to the space have countable network weight. In addition, connections to the class of D-spaces and the class of hereditarily Lindelöf spaces are shown.
A general "in between theorem".
A general invariant metrization theorem for compact spaces
A generalisation of almost-compactness, with an associated generalisation of completeness
A generalization of a contraction principle in probabilistic metric spaces. II.
A generalization of a theorem of Polak
A generalization of boundedly compact metric spaces
A metric space is called a space provided each continuous function on into a metric target space is uniformly continuous. We introduce a class of metric spaces that play, relative to the boundedly compact metric spaces, the same role that spaces play relative to the compact metric spaces.
A groupoid formulation of the Baire Category Theorem
We prove that the Baire Category Theorem is equivalent to the following: Let G be a topological groupoid such that the unit space is a complete metric space, and there is a countable cover of G by neighbourhood bisections. If G is effective, then G is topologically principal.
A lattice of conditions on topological spaces II
A lemma on finite-dimensional covers
A Lindelöf space X such that is normal but not paracompact
A López-Escobar theorem for metric structures, and the topological Vaught conjecture
We show that a version of López-Escobar’s theorem holds in the setting of model theory for metric structures. More precisely, let denote the Urysohn sphere and let Mod(,) be the space of metric -structures supported on . Then for any Iso()-invariant Borel function f: Mod(,) → [0,1], there exists a sentence ϕ of such that for all M ∈ Mod(,) we have . This answers a question of Ivanov and Majcher-Iwanow. We prove several consequences, for example every orbit equivalence relation of a Polish group...
A Mapping Theorem on Aleph-spaces
A Maximality Principle On Ordered Metric Spaces.
A Measurable Selection Theorem for Compact-Valued Maps.
A metric on the space of projections admitting nice isometries
Motivated by the concept of separation between propositions in quantum logic, we introduce the so-called separation metric or Santos metric on the space of all projections in a Hilbert space. We show that the resulting metric space has only "nice" surjective isometries. On the nontrivial projections they are all unitarily or antiunitarily equivalent to the identity or to taking the orthogonal complement. We relate this result to Wigner's classical theorem on the form of quantum mechanical symmetry...
A metric tangential calculus.