Completely regularly ordered spaces versus T 2 - ordered spaces which are completely regular ✩
نویسندگان
چکیده
Schwarz and Weck-Schwarz have shown that a T2-ordered space (X, τ, ) whose underlying topological space (X, τ) is completely regular need not be a completely regularly ordered space (that is, T3.5 + T2-ordered T3.5-ordered). We show that a completely regular T2-ordered space need not be completely regularly ordered even under more stringent assumptions such as convexity of the topology. One example involves the construction of a nontrivial topological ordered space on which every continuous increasing function into the real unit interval is constant. 2003 Elsevier B.V. All rights reserved. MSC: 54F05; 54G20; 54C99; 06F30
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