The structure of Eberlein, uniformly Eberlein and Talagrand compact spaces in Σ()
V. Farmaki (1987)
Fundamenta Mathematicae
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V. Farmaki (1987)
Fundamenta Mathematicae
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J. Siciak (1969)
Annales Polonici Mathematici
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M. K. Aouf (1989)
Matematički Vesnik
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B. Cascales, I. Namioka, J. Orihuela (2003)
Studia Mathematica
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A topological space (T,τ) is said to be fragmented by a metric d on T if each non-empty subset of T has non-empty relatively open subsets of arbitrarily small d-diameter. The basic theorem of the present paper is the following. Let (M,ϱ) be a metric space with ϱ bounded and let D be an arbitrary index set. Then for a compact subset K of the product space the following four conditions are equivalent: (i) K is fragmented by , where, for each S ⊂ D, . (ii) For each countable subset...
Carlos Uzcátegui (2003)
Fundamenta Mathematicae
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Let (X,τ) be a countable topological space. We say that τ is an analytic (resp. Borel) topology if τ as a subset of the Cantor set (via characteristic functions) is an analytic (resp. Borel) set. For example, the topology of the Arkhangel’skiĭ-Franklin space is . In this paper we study the complexity, in the sense of the Borel hierarchy, of subspaces of . We show that has subspaces with topologies of arbitrarily high Borel rank and it also has subspaces with a non-Borel topology....
Jagannath Patel, Ashok Kumar Sahoo (2014)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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The object of the present paper is to solve Fekete-Szego problem and determine the sharp upper bound to the second Hankel determinant for a certain class of analytic functions in the unit disk. We also investigate several majorization properties for functions belonging to a subclass of and related function classes. Relevant connections of the main results obtained here with those given by earlier workers on the subject are pointed out.
A. Bouziad, E. Sukhacheva (2017)
Commentationes Mathematicae Universitatis Carolinae
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For a subset of the real line , Hattori space is a topological space whose underlying point set is the reals and whose topology is defined as follows: points from are given the usual Euclidean neighborhoods while remaining points are given the neighborhoods of the Sorgenfrey line. In this paper, among other things, we give conditions on which are sufficient and necessary for to be respectively almost Čech-complete, Čech-complete, quasicomplete, Čech-analytic and weakly separated...
Aleksander V. Arhangel'skii (2015)
Commentationes Mathematicae Universitatis Carolinae
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We study topological spaces that can be represented as the union of a finite collection of dense metrizable subspaces. The assumption that the subspaces are dense in the union plays a crucial role below. In particular, Example 3.1 shows that a paracompact space which is the union of two dense metrizable subspaces need not be a -space. However, if a normal space is the union of a finite family of dense subspaces each of which is metrizable by a complete metric, then is also metrizable...
Lúcia R. Junqueira, Franklin D. Tall (2003)
Fundamenta Mathematicae
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We consider the question of when , where is the elementary submodel topology on X ∩ M, especially in the case when is compact.
Francesca Acquistapace, A. Díaz-Cano (2011)
Journal of the European Mathematical Society
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We prove that any divisor of a global analytic set has a generic equation, that is, there is an analytic function vanishing on with multiplicity one along each irreducible component of . We also prove that there are functions with arbitrary multiplicities along . The main result states that if is pure dimensional, is locally principal, is not connected and represents the zero class in then the divisor is globally principal.
Mamoru Nunokawa, Emel Yavuz Duman, Shigeyoshi Owa (2013)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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Let denote the class of analytic functions of the form in the open unit disc . Applying the result by S. S. Miller and P. T. Mocanu (J. Math. Anal. Appl. 65 (1978), 289-305), some interesting properties for concerned with Caratheodory functions are discussed. Further, some corollaries of the results concerned with the result due to M. Obradovic and S. Owa (Math. Nachr. 140 (1989), 97-102) are shown.
Maria Elena Becker (2005)
Studia Mathematica
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Let T be a linear operator on a Banach space X with for some 0 ≤ w < 1. We show that the following conditions are equivalent: (i) converges uniformly; (ii) .
Ahmad Al-Omari, Takashi Noiri (2017)
Archivum Mathematicum
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A topological space is said to be -Lindelöf [1] if every cover of by cozero sets of admits a countable subcover. In this paper, we obtain new characterizations and preservation theorems of -Lindelöf spaces.
E. Odell, Th. Schlumprecht, A. Zsák (2007)
Studia Mathematica
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For a countable ordinal α we denote by the class of separable, reflexive Banach spaces whose Szlenk index and the Szlenk index of their dual are bounded by α. We show that each admits a separable, reflexive universal space. We also show that spaces in the class embed into spaces of the same class with a basis. As a consequence we deduce that each is analytic in the Effros-Borel structure of subspaces of C[0,1].
A. D. Rojas-Sánchez, Angel Tamariz-Mascarúa (2016)
Commentationes Mathematicae Universitatis Carolinae
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For a topological property , we say that a space is star if for every open cover of the space there exists such that . We consider space with star countable extent establishing the relations between the star countable extent property and the properties star Lindelöf and feebly Lindelöf. We describe some classes of spaces in which the star countable extent property is equivalent to either the Lindelöf property or separability. An example is given of a Tychonoff star Lindelöf...
Michał Morayne (1987)
Colloquium Mathematicae
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Alan S. Dow (2015)
Commentationes Mathematicae Universitatis Carolinae
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We prove that implies there is a zero-dimensional Hausdorff Lindelöf space of cardinality which has points . In addition, this space has the property that it need not be Lindelöf after countably closed forcing.
S. Gabriyelyan, J. Kąkol, G. Plebanek (2016)
Studia Mathematica
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Following Banakh and Gabriyelyan (2016) we say that a Tychonoff space X is an Ascoli space if every compact subset of is evenly continuous; this notion is closely related to the classical Ascoli theorem. Every -space, hence any k-space, is Ascoli. Let X be a metrizable space. We prove that the space is Ascoli iff is a -space iff X is locally compact. Moreover, endowed with the weak topology is Ascoli iff X is countable and discrete. Using some basic concepts from probability...
Teodor Banica, Ion Nechita, Jean-Marc Schlenker (2014)
Annales mathématiques Blaise Pascal
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We investigate the problem of counting the real or complex Hadamard matrices which are circulant, by using analytic methods. Our main observation is the fact that for the quantity satisfies , with equality if and only if is the eigenvalue vector of a rescaled circulant complex Hadamard matrix. This suggests three analytic problems, namely: (1) the brute-force minimization of , (2) the study of the critical points of , and (3) the computation of the moments of . We explore here...