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Sequential convergence in topological vector spaces [PDF]
Georgian Mathematical Journal, 1995 Abstract For a given linear topology τ, on a vector space E, the finest linear topology having the same τ convergent sequences, and the finest linear topology on E having the same τ precompact sets, are investigated. Also, the sequentially bornological spaces and the sequentially barreled spaces are introduced and some of their ...
V. Benekas, A. K. Katsaras
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2014
The main objective of this chapter is to present an outline of the basic tools of analysis necessary to develop the subsequent chapters. The results addressed include the open mapping and closed graph theorems and an introduction to Hilbert spaces. We assume the reader has a background in linear algebra and elementary real analysis at an undergraduate ...
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The main objective of this chapter is to present an outline of the basic tools of analysis necessary to develop the subsequent chapters. The results addressed include the open mapping and closed graph theorems and an introduction to Hilbert spaces. We assume the reader has a background in linear algebra and elementary real analysis at an undergraduate ...
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2002
In this chapter we describe the basic facts on locally convex vector spaces. We follow the representation given in the textbook of S. Rolewicz [86] and begin with metric and topological spaces.
Ryszard Urbański, Diethard Pallaschke
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In this chapter we describe the basic facts on locally convex vector spaces. We follow the representation given in the textbook of S. Rolewicz [86] and begin with metric and topological spaces.
Ryszard Urbański, Diethard Pallaschke
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2010
Background Topology Valuation Theory Algebra Linear Functionals Hyperplanes Measure Theory Normed Spaces Commutative Topological Groups Elementary Considerations Separation and Compactness Bases at 0 for Group Topologies Subgroups and Products Quotients S-Topologies Metrizability Completeness Completeness Function Groups Total Boundedness Compactness ...
Edward Beckenstein, Lawrence Narici
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Background Topology Valuation Theory Algebra Linear Functionals Hyperplanes Measure Theory Normed Spaces Commutative Topological Groups Elementary Considerations Separation and Compactness Bases at 0 for Group Topologies Subgroups and Products Quotients S-Topologies Metrizability Completeness Completeness Function Groups Total Boundedness Compactness ...
Edward Beckenstein, Lawrence Narici
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2013
A topological vector space X over \(\mathbb{R}\) or \(\mathbb{C}\) is a vector space, which is also a topological space, in which the vector space operations are continuous.
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A topological vector space X over \(\mathbb{R}\) or \(\mathbb{C}\) is a vector space, which is also a topological space, in which the vector space operations are continuous.
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1987
The general theory of topological vector spaces was founded during the period which goes from 1920 to 1930 approximately. But it had been prepared for a long time before by the study of numerous problems of Functional Analysis; and its history cannot be retraced without indicating, at least summarily, how the study of these problems gradually brought ...
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The general theory of topological vector spaces was founded during the period which goes from 1920 to 1930 approximately. But it had been prepared for a long time before by the study of numerous problems of Functional Analysis; and its history cannot be retraced without indicating, at least summarily, how the study of these problems gradually brought ...
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1991
When we use logarithms for practical calculations, we rarely know exactly the numbers with which we are working; never, if they result from any physical operation other than counting. However if the data are about right, so is the answer. To increase the accuracy of the answer, we must increase that of the data (and perhaps, to use this accuracy, refer
Christopher T. J. Dodson, Timothy Poston
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When we use logarithms for practical calculations, we rarely know exactly the numbers with which we are working; never, if they result from any physical operation other than counting. However if the data are about right, so is the answer. To increase the accuracy of the answer, we must increase that of the data (and perhaps, to use this accuracy, refer
Christopher T. J. Dodson, Timothy Poston
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1981
In this chapter we start our investigations on general topological vector spaces by introducing the basic concepts and giving the standard descriptions of linear topologies by means of particular neighbourhood bases of the zero vector. This is followed by a brief discussion of boundedness and of continuity of linear forms in 2.3.
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In this chapter we start our investigations on general topological vector spaces by introducing the basic concepts and giving the standard descriptions of linear topologies by means of particular neighbourhood bases of the zero vector. This is followed by a brief discussion of boundedness and of continuity of linear forms in 2.3.
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2018
There are natural types of convergence on linear spaces of functions with the feature that the convergence cannot be described as convergence with respect to a norm. These are, for instance, pointwise convergence and convergence in measure. Such types of convergence will, with rare exceptions, be the weak and weak\(^*\) convergence in Banach spaces ...
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There are natural types of convergence on linear spaces of functions with the feature that the convergence cannot be described as convergence with respect to a norm. These are, for instance, pointwise convergence and convergence in measure. Such types of convergence will, with rare exceptions, be the weak and weak\(^*\) convergence in Banach spaces ...
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Fuzzy topological vector spaces I
Fuzzy Sets and Systems, 1981This is a continuation of ibid. 6, 85-95 (1981; Zbl 0463.46009). It is shown that a topology \(\tau\), on a vector space E, is linear iff the fuzzy topology \(\omega\) (\(\tau)\), consisting of all \(\tau\)-lower semicontinuous fuzzy sets, is linear. The fuzzy seminormed and the fuzzy normed linear spaces are introduced and some of their properties are
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