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 (in the sense of the metric induced by the absolute value) is nonempty: B 1 ⊇ B 2 ⊇ ⋯ ⇒ ⋂ n ∈ N B n ≠ ∅ . {\displaystyle B_{1}\supseteq B_{2}\supseteq \cdots \Rightarrow \bigcap _{n\in {\mathbf {N} }}B_{n}\neq \emptyset .} 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.

Source: Wikipedia — Spherically complete field (CC BY-SA 4.0)