Title
Pointwise bornological spaces Pointwise bornological spaces
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
Amsterdam ,
Subject
Mathematics
Source (journal)
Topology and its applications. - Amsterdam
Volume/pages
156(2009) :12 , p. 2019-2027
ISSN
0166-8641
ISI
000267388100006
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
With each metric space (X, d) we can associate a bornological space (X, B(d)) where B(d) is the set of all subsets of X with finite diameter. Equivalently, B(d) is the set of all subsets of X that are contained in a ball with finite radius. If the metric d can attain the value infinite, then the set of all subsets with finite diameter is no longer a bornology. Moreover, if d is no longer symmetric, then the set of subsets with finite diameter does not coincide with the set of subsets that are contained in a ball with finite radius. In this text we will introduce two structures that capture the concept of boundedness in both symmetric and non-symmetric extended metric spaces. (C) 2009 Elsevier B.V. All rights reserved.
Full text (open access)
https://repository.uantwerpen.be/docman/irua/8837c0/1314.pdf
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