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FRAGMENTABILITY BY THE DISCRETE METRIC

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

Published online by Cambridge University Press:  05 January 2015

WARREN B. MOORS
WARREN B. MOORS*
Affiliation:
Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland, New Zealand email [email protected]
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Abstract

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In a recent paper, topological spaces $(X,{\it\tau})$ that are fragmented by a metric that generates the discrete topology were investigated. In the present paper we shall continue this investigation. In particular, we will show, among other things, that such spaces are ${\it\sigma}$-scattered, that is, a countable union of scattered spaces, and characterise the continuous images of separable metrisable spaces by their fragmentability properties.

Keywords

fragmentablesigma-scatteredtopological game

MSC classification

Primary: 46B20: Geometry and structure of normed linear spaces
Secondary: 46B22: Radon-Nikodým, Kreĭn-Milman and related properties
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 91 , Issue 2 , April 2015 , pp. 303 - 310
Copyright
Copyright © 2015 Australian Mathematical Publishing Association Inc. 

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