Retractions and Open Mappings between Convex Sets.
We characterize the AR property in convex subsets of metric linear spaces in terms of certain near-selections.
The Blaschke–Kakutani result characterizes inner product spaces , among normed spaces of dimension at least 3, by the property that for every 2 dimensional subspace there is a norm 1 linear projection onto . In this paper, we determine which closed neighborhoods of zero in a real locally convex space of dimension at least 3 have the property that for every 2 dimensional subspace there is a continuous linear projection onto with .
We investigate stability of various classes of topological algebras and individual algebras under small deformations of multiplication.
In this note we characterize the c-paracompact and c-collectionwise normal spaces in terms of continuous selections. We include the usual techniques with the required modifications by the cardinality.