Spherically complete field
In mathematics, a field K with an absolute value is called spherically complete if the intersection of every decreasing sequence of balls is nonempty:
The definition can be adapted also to a field K with a valuation v taking values in an arbitrary ordered abelian group: 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.Examples
