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On the semi-uniformity of bornological convergence
Quaestiones Mathematicae, 2015When in the construction of the ρ-Hausdorff distance the balls with finite radius are replaced with an arbitrary ideal of bounded sets we no longer obtain a uniformity, but a semi-uniformity. In this paper we study the uniform reflection of this structure and its properties.Keywords: Semi-uniformity, pretopology, bornology, bornological convergence ...
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Pseudometrizable bornological convergence is Attouch-Wets convergence
2008Let \(\mathcal S\) be an ideal of subsets of a metric space \((X,d)\). A net of subsets \((A_\lambda)_\lambda\) of \(X\) is called \(\mathcal S\)-convergent to a subset \(A\) of \(X\) if for each \(S\in {\mathcal S}\) and each \(\varepsilon > 0\), we have eventually \(A\cap S\subset A^\varepsilon_\lambda\) and \(A_\lambda\cap S\subset A^\varepsilon ...
Beer, G, LEVI, SANDRO
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Convergence of Filters on Bornological Vector Spaces and Neutrosophic Filters
International Journal of Neutrosophic ScienceIn this research, we construct new type of convergence of bornological vector spaces called convergence of filters through using conception bounded sets. As well, we have considered several characteristics of these concepts like Fréchet filter associated with sequence, filter that has a unique limit and ultra-filter which is very useful in the study of
Fatma Al-Basri, Asawer Khdeidan
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Bornological Convergence and Uniform Convergence of Distance Functionals
2023openaire +1 more source
Bornological convergence and separation in L,M)-fuzzy bornological vector spaces
Liang, Chengyu, Cui, Jieshengopenaire +1 more source