Stable homeomorphisms on infinite-dimensional normed linear spaces.

Abstract

R. Y. T. Wong has recently shown that all homeomorphisms on a connected manifold modeled on infinite-dimensional separable Hilbert space are stable. In this paper we establish the stability of all homeomorphisms on a normed linear space E E such that E E is homeomorphic to the countable infinite product of copies of itself. The relationship between stability of homeomorphisms and a strong annulus conjecture is demonstrated and used to show that stability of all homeomorphisms on a normed linear space E E implies stability of all homeomorphisms on a connected manifold modeled on E E , and that in such a manifold collared E E -cells are tame.