Ball intersection properties in metric spaces

Ball transitive ordered metric spaces

0. Introduction. If (X,≤) is a partially ordered set and A ⊆ X, then the decreasing hull d(A) of A in X is defined to be d(A) = {x ∈ X : x ≤ a for some a ∈ A}. If the poset X is not understood from the context, we may write dX(A). A subset A ⊆ X is a decreasing set if A = d(A). The intersection or union of any collection of decreasing sets in X is again a decreasing set in X. The increasing hul...

On Some Properties of Analytic Spaces Connected with Bergman Metric Ball

Ball Versus Distance Convexity of Metric Spaces

We consider two different notions of convexity of metric spaces, namely (strict/uniform) ball convexity and (strict/uniform) distance convexity. Our main theorem states that (strict/uniform) distance convexity is preserved under a fairly general product construction, whereas we provide an example which shows that the same does not hold for (strict/uniform) ball convexity, not even when consider...

Exploring Intersection Trees for Indexing Metric Spaces

Searching in a dataset for objects that are similar to a given query object is a fundamental problem for several applications that use complex data. The general problem of many similarity measures for complex objects is their computational complexity, which makes them unusable for large databases. Here, we introduce a study of a variant of a metric tree data structure for indexing and querying ...

The Intersection of Topological and Metric Spaces

In this paper we will prove the Urysohn Meterization Theorem, which gives sufficient conditions for a topological space to be metrizable. In the process of proving this theorem, we will the discuss separation and countability axiom of topological spaces and prove the Urysohn Lemma.