Corollary

Tag 09DV, permanent. Cite it as [Bourbaki, Tag 09DV].

Integration, chapter VII, § 1. Construction of a Haar measure

— The topology of a nondiscrete locally compact field admits a countable base.

For, K is the union of compact sets $V_1, V_2, \ldots$ . On the other hand, K is metrizable by Prop. 1 of GT, IX, §3, No. 1. Therefore the topology of K admits a countable base (loc. cit., §2, No. 9, Cor. of Prop. 16).

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

Cited by

Corollary, § 1
Lemma 9, § 3
Proposition 6, § 3

Cites

IX, §3, No. 1
Prop. 1