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Sets invariant under projections onto two dimensional subspaces

Simon Fitzpatrick, Bruce Calvert (1991)

Commentationes Mathematicae Universitatis Carolinae

The Blaschke–Kakutani result characterizes inner product spaces E , among normed spaces of dimension at least 3, by the property that for every 2 dimensional subspace F there is a norm 1 linear projection onto F . In this paper, we determine which closed neighborhoods B of zero in a real locally convex space E of dimension at least 3 have the property that for every 2 dimensional subspace F there is a continuous linear projection P onto F with P ( B ) B .

Small deformations of topological algebras

Mati Abel, Krzysztof Jarosz (2003)

Studia Mathematica

We investigate stability of various classes of topological algebras and individual algebras under small deformations of multiplication.

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