Corollary 2

Tag 02T6, permanent. Cite it as [Bourbaki, Tag 02T6].

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

The function $u\mapsto$ dim Coker( $u$ ) is locally constant on the set $\mathscr{M}(E; F)$ of strict injective morphisms of E into F.

Indeed, one has dim Coker( $u$ ) $=$ ind( $u$ ) for $u\in \mathscr{M}(E; F)$ .

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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