Results 11 to 20 of about 181 (133)
Literature Nots on Bornological Set and Bornological Group
Academic Science JournalIn this work, we explain the basic concepts of bornological structures bornological sets and bornological groups, that solve the problems of boundedness for sets and groups. with some examples and fundamental construction for this structure
Anwar Nooruldeen Imran AI-SAIHI +3 more
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On \(\beta\)-differentiability of norms
Journal of Numerical Analysis and Approximation Theory, 2004 In this note we give some characterizations for the differentiability with respect to a bornology of a continuous convex function. The special case of seminorms is treated.
Valeriu Anisiu
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Extensions defined using bornologies
Applied General Topology, 2013 Many extensions of a space X such that the remainder Y is closed can be constructed as B-extensions, that is, by defining a topology on the disjoint union X [ Y , provided there exists a map, satisfying some conditions, from a basis of Y into the family ...
Alessandro Caterino, M. Cristina Vipera
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Well-posedness, bornologies, and the structure of metric spaces [PDF]
Applied General Topology, 2009 Given a continuous nonnegative functional λ that makes sense defined on an arbitrary metric space (X, d), one may consider those spaces in which each sequence (xn) for which lim n→∞λ(xn) = 0 clusters. The compact metric spaces, the complete metric spaces,
Gerald Beer, Manuel Segura
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Selectors of discrete coarse spaces [PDF]
, 2022 summary:Given a coarse space $(X, \mathcal{E})$ with the bornology $\mathcal B$ of bounded subsets, we extend the coarse structure $\mathcal E$ from $X\times X$ to the natural coarse structure on $(\mathcal B \backslash \lbrace \emptyset\rbrace) \times (\
Protasov, Igor
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BORNOLOGICAL COUNTABLE ENLARGEMENTS [PDF]
Proceedings of the Edinburgh Mathematical Society, 2003 AbstractWe show that for a non-flat bornological space there is always a bornological countable enlargement; moreover, when the space is non-flat and ultrabornological the countable enlargement may be chosen to be both bornological and barrelled. It is also shown that countable enlargements for barrelled or bornological spaces are always Mackey ...
Tweddle, Ian, Saxon, S. A.
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On bornological semigroups [PDF]
2015 International Conference on Research and Education in Mathematics (ICREM7), 2015 In this paper we introduce and study the concept of a bornological semigroup. This generalizes the theory of algebraic semigroup from the algebraic setting to the framework of bornological set. Working with bornological set allows to extend the scope of the latter theory considerably.
A.N. Imran, I. S. Rakhimov
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Soft Bornological Group Acts on Soft Bornological Set
Iraqi Journal of Science, 2023 In this paper, we introduce the notation of the soft bornological group to solve the problem of boundedness for the soft group. We combine soft set theory with bornology space to produce a new structure which is called soft bornological group. So that both the product and inverse maps are soft bounded. As well as, we study the actions of the
Ashwaq F. Abdal +3 more
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A useful algebra for functional calculus [PDF]
, 2018 summary:We show that some unital complex commutative LF-algebra of ${\mathcal {C}}^{(\infty )}$ $\mathbb {N}$-tempered functions on $\mathbb {R}^+$ (M.
Hemdaoui, Mohammed, Mohammed Hemdaoui
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Applied General Topology, 2019 A ballean (or coarse space) is a set endowed with a coarse structure. A ballean X is called normal if any two asymptotically disjoint subsets of X are asymptotically separated.
Igor Protasov
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