Results 291 to 300 of about 574,732 (350)
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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
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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
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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.
M. Osborne
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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.
M. Osborne
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Physical Review Letters, 2022
Optical bound states in the continuum (BICs) are exotic topological defects in photonic crystal slabs, carrying polarization topological vortices in momentum space.
Jiajun Wang, Lei Shi, Jian Zi
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Optical bound states in the continuum (BICs) are exotic topological defects in photonic crystal slabs, carrying polarization topological vortices in momentum space.
Jiajun Wang, Lei Shi, Jian Zi
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1982
Vector spaces will be considered as vector spaces over ℂ unless something else is specified. The symbols Hom(X, Y) resp. Sur(X, Y) will be reserved for sets of continuous homomorphisms resp. surjective homomor-phisms; End(X) is the set of continuous endomorphisms and Aut(E) is the set of continuous automorphisms (bijective and bicontinuous ...
L.V. KANTOROVICH, G.P. AKILOV
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Vector spaces will be considered as vector spaces over ℂ unless something else is specified. The symbols Hom(X, Y) resp. Sur(X, Y) will be reserved for sets of continuous homomorphisms resp. surjective homomor-phisms; End(X) is the set of continuous endomorphisms and Aut(E) is the set of continuous automorphisms (bijective and bicontinuous ...
L.V. KANTOROVICH, G.P. AKILOV
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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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Journal of the London Mathematical Society, 1965
Definition 1. (a) A set E u is said to be a topological vector space (or, in short, a TVS) over a given field K, if E u as a pointset is a topological space and a vector space over K such that the mappings: $$\begin{gathered} (x,y) \to x + y, \hfill \\ (\lambda ,x) \to \lambda x \hfill \\ \end{gathered}$$ are continuous in both variables ...
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Definition 1. (a) A set E u is said to be a topological vector space (or, in short, a TVS) over a given field K, if E u as a pointset is a topological space and a vector space over K such that the mappings: $$\begin{gathered} (x,y) \to x + y, \hfill \\ (\lambda ,x) \to \lambda x \hfill \\ \end{gathered}$$ are continuous in both variables ...
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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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