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- Spherically_complete_field abstract "In mathematics, a field K with an absolute value is called spherically complete if the intersection of every decreasing sequence of balls (in the sense of the metric induced by the absolute value) is nonempty:The definition can be adapted also to a field K with a valuation v taking values in an arbitrary ordered abelian group: (K,v) is spherically complete if every collection of balls that is totally ordered by inclusion has a nonempty intersection.Spherically complete fields are important in nonarchimedean functional analysis, since many results analogous to theorems of classical functional analysis require the base field to be spherically complete.".
- Spherically_complete_field wikiPageID "33175921".
- Spherically_complete_field wikiPageRevisionID "522127910".
- Spherically_complete_field hasPhotoCollection Spherically_complete_field.
- Spherically_complete_field subject Category:Algebra.
- Spherically_complete_field subject Category:Functional_analysis.
- Spherically_complete_field comment "In mathematics, a field K with an absolute value is called spherically complete if the intersection of every decreasing sequence of balls (in the sense of the metric induced by the absolute value) is nonempty:The definition can be adapted also to a field K with a valuation v taking values in an arbitrary ordered abelian group: (K,v) is spherically complete if every collection of balls that is totally ordered by inclusion has a nonempty intersection.Spherically complete fields are important in nonarchimedean functional analysis, since many results analogous to theorems of classical functional analysis require the base field to be spherically complete.".
- Spherically_complete_field label "Spherically complete field".
- Spherically_complete_field sameAs m.0h65960.
- Spherically_complete_field sameAs Q7576719.
- Spherically_complete_field sameAs Q7576719.
- Spherically_complete_field wasDerivedFrom Spherically_complete_field?oldid=522127910.
- Spherically_complete_field isPrimaryTopicOf Spherically_complete_field.