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.
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 ...
Beer, Gerald; Rodríguez López, Jesús(Michigan State University Press, 2010)
A function gg between directed sets ⟨Σ,⪰′⟩⟨Σ,⪰′⟩ and ⟨Λ,⪰⟩⟨Λ,⪰⟩ is called \emph{ultimately increasing} if for each σ1∈Σσ1∈Σ there exists σ2⪰′σ1σ2⪰′σ1 such that σ⪰′σ2⇒g(σ)⪰g(σ1)σ⪰′σ2⇒g(σ)⪰g(σ1). A subnet of a net aa defined ...
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 ...