Continuous functions on a compact Hausdorff space
View article: The Bishop-Phelps-Bollobas property for operators between spaces of continuous functions
The Bishop-Phelps-Bollobas property for operators between spaces of continuous functions Open
We show that the space of bounded linear operators between spaces of continuous functions on compact Hausdorff topological spaces has the Bishop-Phelps-Bollobas property. A similar result is also proved for the class of compact operators f…
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Purely 1-unrectifiable metric spaces and locally flat Lipschitz functions Open
We characterize compact metric spaces whose locally flat Lipschitz functions separate points uniformly as exactly those that are purely 1-unrectifiable, resolving a problem of Weaver. We subsequently use this geometric characterization to …
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Classifying locally compact semitopological polycyclic monoids Open
We present a complete classification of Hausdorff locally compact polycyclic monoids up to a topological isomorphism. A {\em polycyclic monoid} is an inverse monoid with zero, generated by a subset $Λ$ such that $xx^{-1}=1$ for any $x\inΛ$…
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A New Approach to Hausdorff Space Theory via the Soft Sets Open
The aim of this paper is to present the concept of soft bitopological Hausdorff space (SBT Hausdorff space) as an original study. Firstly, I introduce some new concepts in soft bitopological space such as SBT point, SBT continuous function…
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Spaces of Continuous Functions Open
The space C(X) of all continuous functions on a compact space X carries the structure of a normed vector space, an algebra and a lattice. On the one hand we study the relations between these structures and the topology of X, on the other h…
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A Riesz representation theory for completely regular Hausdorff spaces and its applications Open
Let X be a completely regular Hausdorff space, E and F be Banach spaces. Let C b ( X , E ) be the space of all E -valued bounded, continuous functions on X , equipped with the strict topology β . We develop the Riemman-Stieltjes-type Integ…
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Spaces of Continuous Functions Open
This chapter is dedicated to the properties of spaces of continuous functions taking values in a semi-normed space. It presents the definitions of the space of continuous functions, the space of uniformly continuous functions, and variants…
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On Regulated Functions Open
In this paper we investigate the space of regulated functions on a compact interval [0,1]. When equipped with the topology of uniform convergence this space is isometrically isomorphic to some space of continuous functions. We study some o…
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Boundedness of Hausdorff operators on Hardy spaces $H^1$ over locally compact groups Open
Results of Liflyand and collaborators on the boundedness of Hausdorff operators on the Hardy space $H^1$ over finite-dimensional real space generalized to the case of locally compact groups that are spaces of homogeneous type. Special case…
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Spaces of non-additive measures generated by triangular norms Open
We consider non-additive measures on the compact Hausdorff spaces, which are generalizations of the idempotent measures and max-min measures. These measures are related to the continuous triangular norms and they are defined as functionals…
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Purely 1-unrectifiable spaces and locally flat Lipschitz functions Open
For any compact metric space $M$, we prove that the locally flat Lipschitz functions separate points (of $M$) uniformly if and only if $M$ is purely 1-unrectifiable, resolving a problem posed by Weaver in 1999. We subsequently use this geo…
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Compact convex structure of measurements and its applications to simulability, incompatibility, and convex resource theory of continuous-outcome measurements Open
We introduce the post-processing preorder and equivalence relations for general measurements on a possibly infinite-dimensional general probabilistic theory described by an order unit Banach space $E$ with a Banach predual. We define the m…
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De Branges Type Lemma and Approximation in Weighted Spaces Open
The purpose of this paper is to give some generalizations of de Branges Lemma for weighted spaces to obtain different approximation theorems in weighted spaces for algebras, vector subspaces or convex cones. We recall that the (original) d…
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Pełczyński space is isomorphic to the Lipschitz free space over a compact set Open
We prove the result stated in the title. This provides a first example of an infinite-dimensional Banach space whose Lipschitz free space is isomorphic to the free space of a compact set.
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Finite-dimensional complex manifolds on commutative Banach algebras and continuous families of compact complex manifolds Open
Let Γ ( M ) be the set of all global continuous cross sections of a continuous family M of compact complex manifolds on a compact Hausdorff space X . In this paper, we introduce a C ( X )-manifold structure on Γ ( M ). Especially, if X is …
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A note on Hausdorff convergence of pseudospectra Open
For a bounded linear operator on a Banach space, we study approximation of the spectrum and pseudospectra in the Hausdorff distance. We give sufficient and necessary conditions in terms of pointwise convergence of appropriate spectral quan…
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Vietoris topology on hyperspaces associated to a noncommutative compact space Open
We study some topological spaces that can be considered as hyperspaces associated to noncommutative spaces.More precisely, for a NC compact space associated to a unital C * -algebra, we consider the set of closed projections of the second …
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Almost periodic functions on Hausdorff almost periodic time scales Open
This paper is devoted to generalizing the notion of almost periodic functions on time scales. We introduce a new class of almost periodic time scales called Hausdorff almost periodic time scales by using the Hausdorff distance and propose …
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Multiplicative Normed Linear Space and its Topological Properties Open
The aim of this article is to propose a new space called multiplicative normed linear space and discuss different topological properties of this space. We establish equivalence between multiplicative compactness and multiplicative sequenti…
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Certain Types of m-Compact Functions Open
In this work we introduce some functions by using cocompact open sets and semi cocompact open sets in m-structure space namely, m-coc-continuous, m-coc*-continuous, m-coc**-continuous, m-coc-compact, m-s-coc-continuous, m-s-coc*-continuous…
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STRICT TOPOLOGIES AND OPERATORS ON SPACES OF VECTOR-VALUED CONTINUOUS FUNCTIONS Open
Let X be a completely regular Hausdorff space, and E and F be Banach spaces. Let $C_{rc}(X,E)$ be the Banach space of all continuous functions $f:X{\rightarrow}E$ such that f(X) is a relatively compact set in E. We establish an integral re…
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Sequentially Hausdorff and full sequentially Hausdorff spaces Open
In this paper, we define the notions of sequentially HausdorffSpace and full sequentially Hausdorff space. Also we give the relationshipsbetween these notions and Hausdorffness.
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New Results of Normed Approach Space Open
In this work, we introduce a new convergence formula. We also define cluster point , δ-Cauchy sequence, δ-convergent, δ-completeness , and define sequentially contraction in approach space. In addition, we prove the contraction condition i…
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A generalization of Strassen's spectral theorem Open
Given a semiring with a preorder subject to certain conditions, the asymptotic spectrum, as introduced by Strassen (J. reine angew. Math. 1988), is a compact Hausdorff space together with a map from the semiring to the ring of continuous f…
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When is the space of semi-additive functionals an absolute (neighbourhood) retract? Open
In the present paper proved that if for a given compact Hausdorff space X the hyperspace exp(X) is a contractible compact space then the space OSf(X) is also a contractible compact space. As a consequence it is established that the space O…
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Local Hausdorff Measure Open
A local Hausdorff dimension is defined on a metric space. We study its properties and use it to define a local Hausdorff measure. We show that in the case that in the local Hausdorff measure is finite we can recover the global Hausdorff di…
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A functional analysis point of view on compactness theorems in function spaces Open
In the paper, we present a functional view on the Arzel\`a-Ascoli theorem for the Banach space $C_0(X)$, where $X$ is a locally compact Hausdorff space. The proof hinges upon Banach-Alaoglu's theorem. This approach is motivated by the work…
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Standard homogeneous C*-algebras as compact quantum metric spaces Open
Given a compact metric space X and a unital C*-algebra A, we introduce a family of seminorms on the C*-algebra of continuous functions from X to A, denoted C(X, A), induced by classical Lipschitz seminorms that produce compact quantum metr…
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Functional Space Consisted by Continuous Functions on Topological Space Open
Summary In this article, using the Mizar system [1], [2], first we give a definition of a functional space which is constructed from all continuous functions defined on a compact topological space [5]. We prove that this functional space i…
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On potential kernels associated with random dynamical systems Open
Let \\((\\theta,\\varphi)\\) be a continuous random dynamical system defined on a probability space \\((\\Omega,\\mathcal{F},\\mathbb{P})\\) and taking values on a locally compact Hausdorff space \\(E\\). The associated potential kernel \\…