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The stereographic projection in Banach spaces. (English) Zbl 1142.46008

Summary: We give a new and direct proof of the fact that, in any infinite dimensional Banach space, the unit sphere minus any one point is homeomorphic to a closed hyperplane. The proof involves \(L\)-structures and geometric concepts as, for instance, rotund, smooth and exposed points.

MSC:

46B20 Geometry and structure of normed linear spaces
46B99 Normed linear spaces and Banach spaces; Banach lattices
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References:

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