Corollary 2

Tag 04XY, permanent. Cite it as [Bourbaki, Tag 04XY].

Commutative Algebra, chapter VI, § 9. Application: locally compact fields

Every locally compact field is connected or totally disconnected; if it is connected, it is isomorphic to $\mathbf{R}, \mathbf{C}$ or $\mathbf{H}$ .

If the topology on a field $K$ is defined by an ultrametric absolute value, $K$ is totally disconnected with this topology.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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Cites

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