On convergence of closed sets in a metric space and distance functions
Author:
- 1 June 1985
- journal article
- research article
- Published by Cambridge University Press (CUP) in Bulletin of the Australian Mathematical Society
- Vol. 31 (3) , 421-432
Abstract
Let CL(X) denote the nonempty closed subsets of a metric space X. We answer the following question: in which spaces X is the Kuratowski convergence of a sequence {Cn} in CL(X) to a nonempty closed set C equivalent to the pointwise convergence of the distance functions for the sets in the sequence to the distance function for C ? We also obtain some related results from two general convergence theorems for equicontinuous families of real valued functions regarding the convergence of graphs and epigraphs of functions in the family.Keywords
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