Corollary 1

Tag 02T5, permanent. Cite it as [Bourbaki, Tag 02T5].

Théories spectrales, chapter III, § 4. Perturbations dans les espaces de Banach

The functions defined by $u\mapsto$ dim Ker( $u$ ) and by $u\mapsto$ dim Coker( $u$ ) on $\mathscr{Q}\mathscr{M}(E; F)$ are upper semi-continuous. The function $u\mapsto$ ind( $u$ ) is locally constant on $\mathscr{Q}\mathscr{M}(E; F)$ .

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.

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