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

Topology on ordered fields

Yoshio Tanaka (2012)

Commentationes Mathematicae Universitatis Carolinae

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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 .

An uncountable partition contained in the atomless σ-field

Radosław Drabiński (2011)

Colloquium Mathematicae

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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.