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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2009; 46(4): 701-711

Printed July 1, 2009

https://doi.org/10.4134/JKMS.2009.46.4.701

Copyright © The Korean Mathematical Society.

Semicontinuous planar total preorders on non-separable metric spaces

Mar\'ia Jes\'us Campi{\'o}n, Juan Carlos Candeal, and Esteban Indur{\'a}in

Universidad P\'ublica de Navarra, Universidad de Zaragoza, and Universidad P\'ublica de Navarra

Abstract

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We prove that every non-separable connected metric space can be endowed with a total preorder that is order-isomorphic to a non-representable subset of the lexicographic plane and semicontinuous with respect to the metric topology.

Keywords: real-valued functions, metric spaces, semicontinuous total preorders, representability

MSC numbers: Primary 54F05, Secondary 06A06, 54C08, 54C30

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