Let P<sub>0</sub>(X) be the nonempty subsets of a metric space 〈X, d〉,. Some classical convergences in P<sub>0</sub>(X) - such as convergence in Hausdorff distance, Attouch-Wets convergence and Wijsman convergence - have been shown to be compatible with the weak topology on P<sub>0</sub>(X) induced by all gap and excess functionals with fixed left argument ranging in some bornology. Here we consider an arbitrary ideal of subsets of X and compare the gap and excess topology so generated with the corresponding convergence defined in terms of truncations by elements of the ideal. © 2008 Springer Science+Business Media B.V.
Beer, G., Levi, S. (2008). Gap, excess and bornological convergence. SET-VALUED ANALYSIS, 16(4), 489-506 [10.1007/s11228-008-0086-8].
Gap, excess and bornological convergence
LEVI, SANDRO
2008
Abstract
Let P0(X) be the nonempty subsets of a metric space 〈X, d〉,. Some classical convergences in P0(X) - such as convergence in Hausdorff distance, Attouch-Wets convergence and Wijsman convergence - have been shown to be compatible with the weak topology on P0(X) induced by all gap and excess functionals with fixed left argument ranging in some bornology. Here we consider an arbitrary ideal of subsets of X and compare the gap and excess topology so generated with the corresponding convergence defined in terms of truncations by elements of the ideal. © 2008 Springer Science+Business Media B.V.
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