SEMICONTINUOUS PLANAR TOTAL PREORDERS ON NON-SEPARABLE METRIC SPACES

Marla Jesuus Campioon,Juan Carlos Candeal,Esteban Indurain

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY（2009）

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摘要

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.

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关键词

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

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