Results 181 to 190 of about 295,574 (222)

Topological Vector Spaces

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.
Diethard Pallaschke, Ryszard Urbański
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Topological Vector Spaces

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 ...
Lawrence Narici, Edward Beckenstein
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Topological Vector Spaces

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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Topological Vector Spaces

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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Topological vector spaces

1994
One way to think of functional analysis is as the branch of mathematics that studies the extent to which the properties possessed by finite dimensional spaces generalize to infinite dimensional spaces. In the finite dimensional case there is only one natural linear topology.
Charalambos D. Aliprantis, Kim C. Border
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Topological Vector Spaces

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 Terence John Dodson, Timothy Poston   +1 more
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GROUPOIDS IN TOPOLOGICAL VECTOR SPACE

JP Journal of Geometry and Topology, 2015
In this paper, a groupoid, in a sense an internal groupoid, in the category of topological vector spaces is defined and some properties of this groupoid in terms of covering morphisms are studied. It is proved that the fundamental groupoid functor gives rise to a functor from topological vector spaces to the groupoid in vector spaces.
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Initial Topology, Topological Vector Spaces, Weak Topology

2020
The main objective of this chapter is to present the definition of topological vector spaces and to derive some fundamental properties. We will also introduce dual pairs of vector spaces and the weak topology. We start the chapter by briefly recalling concepts of topology and continuity, thereby also fixing notation.
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Super quasi-topological and paratopological vector spaces versus topological vector spaces

In this paper, we introduce the idea of super quasi-topological vector space which is an extension of the concept of topological vector space and investigate some of its basic properties. We extend the existing notion of quasi-topological vector space to all complex vector spaces and investigate the relationship of super quasi-topological vector spaces
Madhu Ram, Bijan Davvaz
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Topological Vector Spaces

1971
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