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Addendum to ‘The Katětov construction modified for a T 0-quasi-metric space’

Published online by Cambridge University Press:  12 November 2014

HANS-PETER A. KÜNZI  and
MANUEL SANCHIS
HANS-PETER A. KÜNZI
Affiliation:
Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, South Africa Email: hans-peter.kunzi@uct.ac.za
MANUEL SANCHIS
Affiliation:
Institut Universitari de Matemàtiques i Aplicacions (IMAC), Universitat Jaume I de Castelló, Spain Email: sanchis@mat.uji.es
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Abstract

It is known that if K is a compact subset of the (separable complete) metric Urysohn space ( ${\mathbb U}$ , d) and f is a Katětov function on the subspace K of ( ${\mathbb U}$ , d), then there is z ∈ ${\mathbb U}$ such that d(z, x) = f(x) for all x ∈ K.

Answering a question of Normann, we show in this article that the supseparable bicomplete q-universal ultrahomogeneous T 0-quasi-metric space (q ${\mathbb U}$ , D) recently discussed by the authors satisfies a similar property for Katětov function pairs on subsets that are compact in the associated metric space (q ${\mathbb U}$ , Ds ).

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