Regular retractions onto finite dimensional convex sets and the AR-property for Roberts spaces
It is proved that if X is an n-dimensional closed covex subset in a linear metric space E, then there is a retraction r: E→X such that ∥x-r(x)∥[?]2(n+1)∥x-X∥ for every x∈E. This fact is applied to study the AR-property in linear metric spaces. We identify a class of Roberts spaces with the AR-property. We also give a direct proof that for every p∈(0.1),Lp is a needle point space.
- Tsukuba journal of mathematics
Tsukuba journal of mathematics 20(2), 281-289, 1997-01-10