Abstract

Prelude: Love, hate, and exponentials Paths and homotopies The winding number Topology of the plane Integrals and the winding number Vector fields and the rotation number The winding number in functional analysis Coverings and the fundamental group Coda: The Bott periodicity theorem Linear algebra Metric spaces Extension and approximation theorems Measure zero Calculus on normed spaces Hilbert space Groups and graphs Bibliography Index

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