Rings of continuous functions with values in a non-archimedean ordered field

G. De Marco; M. Richter

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Displaying similar documents to “Rings of continuous functions with values in a non-archimedean ordered field”

Topology on ordered fields

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An ordered field is a field which has a linear order and the order topology by this order. For a subfield $F$ of an ordered field, we give characterizations for $F$ to be Dedekind-complete or Archimedean in terms of the order topology and the subspace topology on $F$ .

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Rings of continuous functions with values in an archimedean ordered field

G. de Marco, R. G. Wilson (1970)

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An uncountable partition contained in the atomless σ-field

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This short note considers the question of whether every atomless σ-field contains an uncountable partition. The paper comments the situation for a couple of known σ-fields. A negative answer to the question is the main result.