Caterino, Alessandro; Vipera, M. Cristina(Universitat Politècnica de València, 2011-10-01)

[EN] Many extensions of a space X such that the remainder Y is closed can be constructed as B-extensions, that is, by defining a topology on the disjoint union X [ Y , provided there exists a map, satisfying some conditions, ...

Protasov, Igor(Universitat Politècnica de València, 2019-04-01)

[EN] A ballean (or coarse space) is a set endowed with a coarse structure. A ballean X is called normal if any two asymptotically disjoint subsets of X are asymptotically separated. We say that a ballean X is ultra-normal ...

Krebs, Mike(Universitat Politècnica de València, 2017-04-03)

[EN] We show that there exists a Hausdorff topology on the set R of real numbers such that a subset A of R has compact closure if and only if A is countable. More generally, given any set X and any infinite set S, we prove ...

Beer, Gerald(Universitat Politècnica de València, 2008-04-01)

[EN] This paper looks at some possible ways of equipping a countable product of unbounded metric spaces with a metric that acknowledges the boundedness characteristics of the factors.

Pajoohesh, Homeira(Universitat Politècnica de València, 2022-04-01)

[EN] Bornologies abstract the properties of bounded sets of a metric space. But there are unbounded bornologies on a metric space like $\mathcal{P}(\RR)$ with the Euclidean metric. We show that by replacing $[0,\infty)$ ...

Beer, Gerald(Universitat Politècnica de València, 2010-10-01)

[EN] In this paper we extend the theory of strong uniform continuity and strong uniform convergence, developed in the setting of metric spaces in, to the uniform space setting, where again the notion of shields plays a key ...

Vroegrijk, Tom(Universitat Politècnica de València, 2009-10-01)

[EN] Bornological universes were introduced some time ago by Hu and obtained renewed interest in recent articles on convergence in hyperspaces and function spaces and optimization theory. One o fHu's results gives us a ...

Beer, Gerald; Segura, Manuel(Universitat Politècnica de València, 2009-04-01)

[EN] Given a continuous nonnegative functional λ that makes sense defined on an arbitrary metric space (X, d), one may consider those spaces in which each sequence (xn) for which lim n→∞λ(xn) = 0 clusters. The compact ...