Proposition 7

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

General Topology, chapter IV, § 5. Real-valued functions

Let $f$ be a real-valued function defined on $X$ . If $A$ and $B$ are two non-empty subsets of $X$ such that $A \subset B$ , then

\sup_{x \in A} f(x) \leq \sup_{x \in B} f(x).

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

Cited by

Nothing.