Spherically complete field
id:
spherically-complete-field-182-18629812
title:
Spherically complete field
text:
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:
- B 1 ⊇ B 2 ⊇ ⋯ ⇒ ⋂ n ∈ N B n ≠ ∅. 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. Spherica
brand slug:
wiki
category slug:
encyclopedia
description:
Mathematical term
original url:
https://en.wikipedia.org/wiki/Spherically_complete_field
date created:
2011-09-22T16:12:17Z
date modified:
2024-09-06T18:37:55Z
main entity:
{"identifier":"Q7576719","url":"https://www.wikidata.org/entity/Q7576719"}
image:
fields total:
13
integrity:
15