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Spheres in infinite-dimensional normed spaces are Lipschitz contractible. (English) Zbl 0518.46010

MSC:
46B20 Geometry and structure of normed linear spaces
47H10 Fixed-point theorems
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[1] C. Bessaga and A. Pełczyński, Selected topics in infinite dimensional topology, PWN, Warsaw, 1975. · Zbl 0304.57001
[2] Mahlon M. Day, Normed linear spaces, 3rd ed., Springer-Verlag, New York-Heidelberg, 1973. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 21. · Zbl 0268.46013
[3] K. Goebel, On the minimal displacement of points under Lipschitzian mappings, Pacific J. Math. 45 (1973), 151 – 163. · Zbl 0265.47046
[4] K. Goebel and W. A. Kirk, A fixed point theorem for transformations whose iterates have uniform Lipschitz constant, Studia Math. 47 (1973), 135 – 140. · Zbl 0265.47044
[5] Bogdan Nowak, On the Lipschitzian retraction of the unit ball in infinite-dimensional Banach spaces onto its boundary, Bull. Acad. Polon. Sci. Sér. Sci. Math. 27 (1979), no. 11-12, 861 – 864 (1981) (English, with Russian summary). · Zbl 0472.54008
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