Example 3
Tag 03VS, permanent. Cite it as [Bourbaki, Tag 03VS].
Theory of Sets, chapter IV, § 2. Morphisms and derived structures
Let V, V' be two topologies on the same set A. To say that V is finer than V' means, by virtue of the definition of morphisms in this case (no. 1, Example 3), that ; in other words, every subset of A which is an open set in the topology V' is also an open set in the topology V (and thus, the finer the topology, the more open sets there are).
Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.
Cited by
Nothing.