Leray–Schauder degree

In mathematics, the Leray–Schauder degree is an extension of the degree of a base point preserving continuous map between spheres

or equivalently to boundary-sphere-preserving continuous maps between balls

to boundary-sphere-preserving maps between balls in a Banach space

, assuming that the map is of the form

is some compact map (i.e. mapping bounded sets to sets whose closure is compact).

[1] The degree was invented by Jean Leray and Juliusz Schauder to prove existence results for partial differential equations.

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