Pointwise bornological spaces
Faculty of Sciences. Mathematics and Computer Science

article

2009
Amsterdam
, 2009

Mathematics

Topology and its applications. - Amsterdam

156(2009)
:12
, p. 2019-2027

0166-8641

000267388100006

E

English (eng)

University of Antwerp

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.

https://repository.uantwerpen.be/docman/irua/8837c0/1314.pdf

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