Bourbaki

Example

Tag 0B07, permanent. Cite it as [Bourbaki, Tag 0B07].

General Topology, chapter I, § 2. Continuous functions

\* The mapping f:x→1/(1+x2)f : x \to 1/(1 + x^2) of R\mathbf{R} into itself is continuous, but f(R)f(\mathbf{R}) is the half-open interval ]0,1]]0, 1], which is neither open nor closed in R\mathbf{R}. \*

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

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Cites

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Transcribed from the printed volume. Not translated.