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Three space property for σ-fragmentability

Part of: Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  26 February 2010

Nadezhda K. Ribarska
Nadezhda K. Ribarska
Affiliation:
Sofia University, Department of Mathematics and Informatics, J. Bourchier str. 5, 1126 Sofia, Bulgaria.
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Extract

Let X be a Hausdorff topological space and let ρ be a metric on it, not necessarily related to the topology. The space X is said to be fragmented by the metric ρ if each nonempty set in X has nonempty relatively open subsets of arbitrary small ρ-diameter. This concept was introduced by Jayne and Rogers (see [2]) while they studied the existence of Borel selections for upper semicontinuous set-valued maps.

MSC classification

Secondary: 46B22: Radon-Nikodým, Kreĭn-Milman and related properties
Type
Research Article
Information
Mathematika , Volume 45 , Issue 1 , June 1998 , pp. 113 - 118
Copyright
Copyright © University College London 1998

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References

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