On a form of Ascoli's theorem in locally uniform spaces
Papatriantafillou, Errikos (1989)
Portugaliae mathematica
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Displaying similar documents to “Uniform quotients of metric spaces”
On a form of Ascoli's theorem in locally uniform spaces
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In this article, we formalize in Mizar [1] the notion of uniform space introduced by André Weil using the concepts of entourages [2]. We present some results between uniform space and pseudo metric space. We introduce the concepts of left-uniformity and right-uniformity of a topological group. Next, we define the concept of the partition topology. Following the Vlach’s works [11, 10], we define the semi-uniform space induced by a tolerance and the uniform space induced by an equivalence...
Dirichlet series and uniform ergodic theorems for linear operators in Banach spaces
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We study the convergence properties of Dirichlet series for a bounded linear operator T in a Banach space X. For an increasing sequence of positive numbers and a sequence of functions analytic in neighborhoods of the spectrum σ(T), the Dirichlet series for is defined by D[f,μ;z](T) = ∑n=0∞ e-μnz fn(T), z∈ ℂ. Moreover, we introduce a family of summation methods called Dirichlet methods and study the ergodic properties of Dirichlet averages for T in the uniform operator topology. ...