Proposition 5

Tag 0C2L, permanent. Cite it as [Bourbaki, Tag 0C2L].

General Topology, chapter IX, § 2. Metric spaces and metrizable spaces

Let $f$ be a function defined on a subset $X$ of a topological space $Y$ , taking its values in a complete metric space $X'$ . Then $f$ has a limit relative to $X$ at a point $x \in \overline{X}$ if and only if the oscillation of $f$ at $x$ is zero.

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

Cited by

Nothing.

Cites

Nothing.