Properties of the Holmes space

V. P. Fonf, P. Wojtaszczyk

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

The following properties of the Holmes space H are established: (i)H has the Metric Approximation Property (MAP).(ii)The w*-closure of the set of extreme points of the unit ball BH* of the dual space H* is the whole ball BH*. A family of compact subsets X ⊂ U of the Urysohn space is described such that the Lipschitz-free space F (X) has a finite-dimensional decomposition and is not complemented in H.

Original languageEnglish
Pages (from-to)1627-1633
Number of pages7
JournalTopology and its Applications
Volume155
Issue number14
DOIs
StatePublished - 15 Aug 2008

Keywords

  • Extreme points
  • Holmes space
  • Metric approximation property
  • Non-complemented subspaces
  • Urysohn space

ASJC Scopus subject areas

  • Geometry and Topology

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