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Zbl 0714.03044
Morillon, Marianne
Ensembles totalement ordonnés et axiomes de choix. (Totally ordered sets and axioms of choice). (French)
[J] Sémin. Anal., Univ. Blaise Pascal 1987-1988, No.5, 15 p. (1988).

E. van Dowen has constructed a model of ZF in which there exists a linearly ordered set with non-normal order topology. The axiom of choice implies the existence of a normality operator in every linearly ordered set. The author answers affirmatively a question raised by E. van Douwen whether the assertion that every linearly ordered set has the normal order topology implies the existence of a normality operator, in every linearly ordered set (in ZF). Moreover, several equivalent assertions are shown.
[L.Bukovský]

MSC 2000:: *03E25 Axiom of choice and related propositions (logic)
54A35 Consistency and independence results (general topology)
06F30 Order topologies (order-theoretic aspects)

Keywords: normal topological space; linearly ordered set; axiom of choice; order topology; normality operator

Cited in: Zbl 0724.03031

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