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FRAGMENTABILITY BY THE DISCRETE METRIC

Published online by Cambridge University Press:  05 January 2015

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.

Type
Research Article
Copyright
Copyright © 2015 Australian Mathematical Publishing Association Inc. 

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