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Fuzzy Sets and Systems, ISSN 0165-0114, 07/2016, Volume 294, pp. 93 - 104
In M. Abel and A. Šostak (2011) [1], the concept of an L-fuzzy bornology was introduced. Actually, an L-fuzzy bornology on a set X is a certain ideal in the... 
Bounded mapping | L-valued bornology | Bornology | Fuzzy (pseudo-)metric | Fuzzy topology | Relative compactness set | L-fuzzy bornology | MATHEMATICS, APPLIED | STATISTICS & PROBABILITY | COMPUTER SCIENCE, THEORY & METHODS | Fuzzy (pseudo-) metric | Axioms | Fuzzy set theory | Fuzzy
Journal Article
Journal of Convex Analysis, ISSN 0944-6532, 2015, Volume 22, Issue 4, pp. 1041 - 1060
Hu's metrization theorem for bornological universes is shown to hold in ZF and it is adapted to a quasi-metrization theorem for bornologies in bitopological... 
Bitopological space | Quasi-metric | Bornology | bitopological space | MATHEMATICS | quasi-metric
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2012, Volume 387, Issue 2, pp. 770 - 775
We continue the study of topologies of strong uniform convergence on bornologies initiated by Beer and Levi (2009) [4]. In Beer and Levi (2009) [4] the... 
Bornology | Complete metrizability | Shield | Topology of strong uniform convergence on bornology | MATHEMATICS | MATHEMATICS, APPLIED | Beer
Journal Article
Matematychni Studii, ISSN 1027-4634, 2018, Volume 49, Issue 1, pp. 13 - 18
Journal Article
Applied general topology, ISSN 1989-4147, 2019, Volume 20, Issue 1, pp. 297 - 305
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... 
coarse structure | bornology | extremely normal ballean | maximal ballean | Ballean | ultranormal ballean
Journal Article
Rendiconti del Circolo Matematico di Palermo, ISSN 0009-725X, 08/2019, Volume 68, Issue 2, pp. 339 - 353
Journal Article
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica, ISSN 1024-7696, 2013, Volume 72-73, Issue 2-3, pp. 5 - 16
Journal Article
Iranian Journal of Fuzzy Systems, ISSN 1735-0654, 2011, Volume 8, Issue 1, pp. 19 - 28
The concept of an L-bornology is introduced and the theory of L-bornological spaces is being developed. In particular the lattice of all L-bornologies on a... 
Bornology | L-set | Fuzzy set | Fuzzy topology | L-bornology | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2009, Volume 350, Issue 2, pp. 568 - 589
Let B be an ideal of subsets of a metric space 〈 X , d 〉 . This paper considers a strengthening of the notion of uniform continuity of a function restricted to... 
Uniform convergence | Strong uniform convergence | Strong uniform continuity | Oscillation | Bornology | UC set | Uniform continuity | TOPOLOGY | MATHEMATICS, APPLIED | DISTANCE | BOUNDEDNESS | MATHEMATICS | CONVERGENCE
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2010, Volume 371, Issue 1, pp. 384 - 392
In 1883 Arzelà (1983/1984) [2] gave a necessary and sufficient condition via quasi-uniform convergence for the pointwise limit of a sequence of real-valued... 
Strong continuity | Bornology | Arzelà's quasi-uniform convergence | Strong uniform convergence | Pointwise and uniform convergence | TOPOLOGY | MATHEMATICS | MATHEMATICS, APPLIED | Arzela's quasi-uniform convergence | CONTINUITY | SPACES | Beer
Journal Article
Applied General Topology, ISSN 1576-9402, 2017, Volume 18, Issue 1, pp. 107 - 115
We show that there exists a Hausdorff topology on the set R of real numbers such that a subset A of R has compact closure if and only if A is countable. More... 
Compact closure | Topology | Cardinality | Hausdorff | Hausdorff cardinality | bornology | compact closure | topology
Journal Article
HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, 2019, Volume 48, Issue 6, pp. 1653 - 1666
A concept of quasi-metrizability with respect to a bornology of a generalized topological space in the sense of Delfs and Knebusch is introduced.... 
MATHEMATICS | quasi-metric | STATISTICS & PROBABILITY | topological category | Delfs-Knebusch generalized topological space | bornology
Journal Article
Set-valued and variational analysis, ISSN 1877-0541, 2017, Volume 26, Issue 1, pp. 49 - 65
Journal Article
Topology and its Applications, ISSN 0166-8641, 01/2014, Volume 161, Issue 1, pp. 330 - 342
The bornological convergence structures that have been studied recently as generalizations of Attouch–Wets convergence define pretopologies on hyperspaces. In... 
Bornological convergence | Pretopological space | Bornology | Hausdorff distance | Hyperspace topology | MATHEMATICS | MATHEMATICS, APPLIED | CONVERGENCES
Journal Article
Communications in Mathematical Physics, ISSN 0010-3616, 12/2014, Volume 332, Issue 3, pp. 1345 - 1380
Journal Article
Applied General Topology, ISSN 1989-4147, 2009, Volume 10, Issue 2, pp. 277 - 287
Bornological universes were introduced some time ago by Hu and obtained renewed interest in recent articles on convergence in hyperspaces and function spaces... 
Bornology; uniform space; totally bounded; realcompactness | Uniform space | Bornology | Totally bounded | Realcompactness
Journal Article
Applied general topology, ISSN 1576-9402, 07/2013, Volume 12, Issue 2, pp. 81 - 94
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 [... 
B-extension | Bornology | Topological extension | Boundedness
Journal Article
Topology and its Applications, ISSN 0166-8641, 09/2016, Volume 210, pp. 317 - 354
We introduce the notions of extended topological vector spaces and extended seminormed spaces, following the main ideas of extended normed spaces, which were... 
Seminorms | Topological vector spaces | Extended norms | Extended seminorms | Bornologies | Projective limits | Topological groups | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Topology and its Applications, ISSN 0166-8641, 04/2015, Volume 184, pp. 16 - 28
In this paper, we continue the study of function spaces equipped with topologies of (strong) uniform convergence on bornologies initiated by Beer and Levi [3].... 
Baire | Monotonically p-space | [formula omitted]-Point | Completely metrizable | Strong uniform convergence | Bornology | Strongly Baire | Point | MATHEMATICS | MATHEMATICS, APPLIED | CONTINUITY | qD-Point | STRONG UNIFORM-CONVERGENCE
Journal Article
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