Results 281 to 290 of about 290,651 (321)
Some of the next articles are maybe not open access.
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
openaire +1 more source
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
openaire +1 more source
1999
While normed linear spaces presently appear to be sufficiently general for most theoretical work in economics, mathematicians have found the more general concept of a topological vector space to be quite useful. Consequently, it appears to be very worthwhile for us to be familiar with at least the rudiments of the theory of such spaces. In this chapter
H. H. Schaefer, M. P. Wolff
+4 more sources
While normed linear spaces presently appear to be sufficiently general for most theoretical work in economics, mathematicians have found the more general concept of a topological vector space to be quite useful. Consequently, it appears to be very worthwhile for us to be familiar with at least the rudiments of the theory of such spaces. In this chapter
H. H. Schaefer, M. P. Wolff
+4 more sources
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.
openaire +1 more source
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.
openaire +1 more source
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
openaire +2 more sources
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
openaire +2 more sources
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 ...
openaire +1 more source
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 ...
openaire +1 more source
TOPOLOGICAL SPACES AND VECTOR LATTICES
Russian Mathematical Surveys, 1980Veksler, A. I., Zakharov, V. K.
openaire +2 more sources
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
openaire +1 more source
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
openaire +1 more source
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 +1 more
openaire +1 more source
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 +1 more
openaire +1 more source
Responsive materials architected in space and time
Nature Reviews Materials, 2022Xiaoxing Xia +2 more
exaly
The biofilm matrix: multitasking in a shared space
Nature Reviews Microbiology, 2022Hans-Curt Flemming +2 more
exaly