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${\cal d}$-modified vietoris topology

Proceedings of the London Mathematical Society (1)

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SELECTIONS FOR VIETORIS-LIKE HYPERSPACE TOPOLOGIES
VALENTIN GUTEV, TSUGUNORI NOGURA
Journal:

Proceedings of the London Mathematical Society / Volume 80 / Issue 1 / January 2000

Published online by Cambridge University Press:

01 January 2000, pp. 235-256

Print publication:

January 2000
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A general selection theorem for a Vietoris-like hyperspace topology is obtained and, as a result, several known selection theorems for both `topology'- and `metric'-generated hyperspace topologies are improved from a common point of view. Applications are presented in characterizing classes of metrizable spaces by continuous selections for their hyperspaces.
1991 Mathematics Subject Classification: primary 54B20, 54C65; secondary 54E45, 54D65, 54E40, 54C10, 54G12.