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Real normed space
 Formalized Mathematics
, 1991
"... Summary. We construct a real normed space 〈V, �.�〉, where V is a real vector space and �. � is a norm. Auxillary properties of the norm are proved. Next, we introduce a notion of sequence in the real normed space. The basic operations on sequences (addition, subtraction, multiplication by real numbe ..."
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Cited by 31 (0 self)
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Summary. We construct a real normed space 〈V, �.�〉, where V is a real vector space and �. � is a norm. Auxillary properties of the norm are proved. Next, we introduce a notion of sequence in the real normed space. The basic operations on sequences (addition, subtraction, multiplication by real
On Generalized Probabilistic Normed Spaces
"... In this paper, generalized probabilistic nnormed spaces are studied, topological properties of these spaces are given. As examples, spaces of random variables are considered. Connections with generalized deterministic nnormed spaces are also given. ..."
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In this paper, generalized probabilistic nnormed spaces are studied, topological properties of these spaces are given. As examples, spaces of random variables are considered. Connections with generalized deterministic nnormed spaces are also given.
Normability of probabilistic normed spaces
"... Abstract. Relying on Kolmogorov’s classical characterization of normable topological vector spaces, we study the normability of those probabilistic normed spaces that are also topological vector spaces and provide a characterization of normable Šerstnev spaces. We also study the normability of othe ..."
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Abstract. Relying on Kolmogorov’s classical characterization of normable topological vector spaces, we study the normability of those probabilistic normed spaces that are also topological vector spaces and provide a characterization of normable Šerstnev spaces. We also study the normability
Real Normed Space
"... Summary. We construct a real normed space 〈V, �.�〉, where V is a real vector space and �. � is a norm. Auxillary properties of the norm are proved. Next, we introduce the notion of sequence in the real normed space. The basic operations on sequences (addition, substraction, multiplication by real nu ..."
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Summary. We construct a real normed space 〈V, �.�〉, where V is a real vector space and �. � is a norm. Auxillary properties of the norm are proved. Next, we introduce the notion of sequence in the real normed space. The basic operations on sequences (addition, substraction, multiplication by real
NORMABILITY OF PROBABILISTIC NORMED SPACES
, 2004
"... Abstract. Relying on Kolmogorov’s classical characterization of normable Topological Vector spaces, we study the normability of those Probabilistic Normed Spaces that are also Topological Vector spaces and provide a characterization of normable ˇ Serstnev spaces. We also study the normability of oth ..."
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Abstract. Relying on Kolmogorov’s classical characterization of normable Topological Vector spaces, we study the normability of those Probabilistic Normed Spaces that are also Topological Vector spaces and provide a characterization of normable ˇ Serstnev spaces. We also study the normability
Random 2normed spaces
 Sem. on Probab. Theory Appl. Univ. of Timi¸soara
, 1988
"... Abstract. In [16] K. Menger proposed the probabilistic concept of distance by replacing the number d(p, q), as the distance between points p, q, by a distribution function Fp,q. This idea led to development of probabilistic analysis [3], [11] [18]. In this paper, generalized probabilistic 2normed s ..."
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Cited by 11 (0 self)
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spaces are studied and topological properties of these spaces are given. As an example, a space of random variables is considered, connections with the generalized deterministic 2normed spaces studied in [14] being also given.
Complemented Subspaces in the Normed Spaces
"... The purpose of this paper is to introduce and discuss the concept of orthogonality in normed spaces. A concept of orthogonality on normed linear space was introduced. We obtain some subspaces of Banach spaces which are topologically complemented. ..."
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The purpose of this paper is to introduce and discuss the concept of orthogonality in normed spaces. A concept of orthogonality on normed linear space was introduced. We obtain some subspaces of Banach spaces which are topologically complemented.
BOUNDEDNESS AND SURJECTIVITY IN NORMED SPACES
, 2008
"... We define the (w ∗) boundedness property and the (w ∗) surjectivity property for sets in normed spaces. We show that these properties are pairwise equivalent in complete normed spaces by characterizing them in terms of a categorylike property called (w ∗) thickness. We give examples of interes ..."
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Cited by 4 (3 self)
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We define the (w ∗) boundedness property and the (w ∗) surjectivity property for sets in normed spaces. We show that these properties are pairwise equivalent in complete normed spaces by characterizing them in terms of a categorylike property called (w ∗) thickness. We give examples
On Equilateral Simplices in Normed Spaces
, 1997
"... : It is the aim of this note to improve the lower bound for the problem of Petty on the existence of equilateral simplices in normed spaces. We show that for each k there is a d(k) such that each normed space of dimension d d(k) contains k points at pairwise distance one, and that if the norm is su ..."
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Cited by 1 (0 self)
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: It is the aim of this note to improve the lower bound for the problem of Petty on the existence of equilateral simplices in normed spaces. We show that for each k there is a d(k) such that each normed space of dimension d d(k) contains k points at pairwise distance one, and that if the norm
SHEAF REPRESENTATION OF NORMED SPACES
"... Abstract. A multisorted limtheory, which has as Setvalued models all normed spaces over some specified fields, is introduced. We show that coherent extensions of this limtheory are expressive enough to characterise, for example, the Lpspaces. The sheafvalued spectra, corresponding to the cohe ..."
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Abstract. A multisorted limtheory, which has as Setvalued models all normed spaces over some specified fields, is introduced. We show that coherent extensions of this limtheory are expressive enough to characterise, for example, the Lpspaces. The sheafvalued spectra, corresponding
Results 1  10
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547,062