Proposition 9

Tag 0B4J, permanent. Cite it as [Bourbaki, Tag 0B4J].

General Topology, chapter I, § 6. Filters

An ultrafilter $U$ on a set $X$ induces a filter on a subset $A$ of $X$ if and only if $A \in U$ ; and if this condition is satisfied then $U_A$ is an ultra-filter on $A$ .

This is an immediate consequence of Propositions 5 and 6 of no. 4.

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

Cited by

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Cites

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