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

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 $F$ .

Some remarks on ordered fields

Masayoshi Nagata (1974-1975)

Séminaire Dubreil. Algèbre et théorie des nombres

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Real commutative algebra (II). Plane curves.

D. W. Dubois, A. Bukowski (1979)

Revista Matemática Hispanoamericana

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On full cover property of ordered fields

Tibor Šalát (1994)

Mathematica Slovaca

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Rings of continuous functions with values in an archimedean ordered field

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

Rendiconti del Seminario Matematico della Università di Padova

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On extension of a given finitely additive field-valued, non negative measure, on a finitely additive Boolean tribe, to another tribe more ample

Otton Martin Nikodým (1956)

Rendiconti del Seminario Matematico della Università di Padova

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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.