Title




Pointwise bornological spaces


Author






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 nonsymmetric extended metric spaces. (C) 2009 Elsevier B.V. All rights reserved. 


Language




English


Source (journal)




Topology and its applications.  Amsterdam


Publication




Amsterdam
:
2009


ISSN




01668641


Volume/pages




156
:12
(2009)
, p. 20192027


ISI




000267388100006


Full text (Publisher's DOI)






Full text (open access)





