We show that it is consistent relative to a weakly compact cardinal strong homology additive and compactly supported within the class of locally separable metric spaces. This complements work Mardešić Prasolov [14] showing Continuum Hypothesis implies countable sum Hawaiian earrings witnesses failure possess either these properties. Our results build directly on Lambie-Hanson second author [3] ...

considering the increasing interest in fuzzy theory and possible applications,the concept of fuzzy metric space concept has been introduced by severalauthors from different perspectives. this paper interprets the theory in termsof metrics evaluated on fuzzy numbers and defines a strong hausdorff topology.we study interrelationships between this theory and other fuzzy theories suchas intuitionis...

Contents 1. Introduction 2 2. Metric type 7 2.1. Type for metric spaces 8 2.2. The geometric puzzle 11 2.3. Pisier's argument 12 2.4. Unique obstructions to type 17 3. Metric cotype 19 4. Markov type and cotype 22 4.1. Lipschitz extension via Markov type and cotype 27 5. Markov convexity 29 6. Metric smoothness? 32 7. Bourgain's discretization problem 32 8. Nonlinear Dvoretzky theorems 33 8.1. ...

In locally compact spaces, (Borel-)measurable sets can be approximated by compact sets. Ulam extended this result to complete separable metric spaces. We give a constructive proof of Ulam’s theorem. It is first proved intuitionistically and then, using a logical ‘trick’ due to Ishihara, a proof acceptable in Bishop-style mathematics is obtained. We feel this proof provides some insight into Ish...

The general notion of topology does not allow to compare neighborhoods of different points. Such a comparison is quite natural in various geometric contexts. The general setting for such a comparison is that of a uniform structure. The most common and natural way for a uniform structure to appear is via a metric, which was already mentioned on several occasions in Chapter 1, so we will postpone...

In 1944, McKinsey and Tarski proved that S4 is the logic of the topological interior and closure operators of any separable dense-in-itself metric space. Thus, the logic of topological interior and closure over arbitrary metric spaces coincides with the logic of the real line, the real plane, and any separable dense-in-itself metric space; it is finitely axiomatisable and PSpace-complete. Becau...

The main goal of this paper is to show that the inductive dimension of a σ-compact metric space X can be characterized in terms of algebraical sums of connectivity (or Darboux) functions X → R. As an intermediate step we show, using a result of Hayashi [9], that for any dense Gδ set G ∈ R the union of G and some k homeomorphic images of G is universal for k-dimensional separable metric spaces. ...

in this work‎, ‎we formulate chatterjea contractions using graphs in metric spaces endowed with a graph ‎‎and‏ ‎‎‎‎investigate ‎the ‎existence‎ ‎of ‎fixed ‎points ‎for such mappings ‎under two different hypotheses‎. we also discuss the uniqueness of the fixed point. the given result is a generalization of chatterjea's fixed point theorem from metric spaces to metric spaces endowed with a graph.