Electronic Version 19 (1994), 15-35

Czeslaw Bessaga

We recall some explicit formulas of analytic character which were invented during the process of formation of infinite-dimensional topology, and present some applications of them. The following topics are covered:

A. Radial homeomorphisms and retractions of convex bodies; analogues of gauge functionals and radial retractions for Banach lattices. Applications: Lipschitz retraction onto c₀ (Lindenstrauss) and lack of fixed points for Lipschitz self-maps of non compact convex sets (Lin-Sternfeld).

B. Non-complete-norm deleting homeomorphisms and diffeomorphisms with applications (Garay) to ordinary differential equations. An analogy with West's theorem on fixed point sets of transformation groups.

C. The coordinate switching technique: a ``simultaneous'' proof of West's theorem and the Ribe-Aharoni-Lindenstrauss example of uniformly homeomorphic and not Lipschitz homeomorphic separable Banach spaces.

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volume 19: table of contents
topology proceedings Electronic Version