Properties of the Holmes space

V. P. Fonf; P. Wojtaszczyk

doi:10.1016/j.topol.2008.03.008

Properties of the Holmes space

V. P. Fonf, P. Wojtaszczyk

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

7 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 B_H* of the dual space H^* is the whole ball B_H*. 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 language	English
Pages (from-to)	1627-1633
Number of pages	7
Journal	Topology and its Applications
Volume	155
Issue number	14
DOIs	https://doi.org/10.1016/j.topol.2008.03.008
State	Published - 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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10.1016/j.topol.2008.03.008

Cite this

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title = "Properties of the Holmes space",

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.",

keywords = "Extreme points, Holmes space, Metric approximation property, Non-complemented subspaces, Urysohn space",

author = "Fonf, {V. P.} and P. Wojtaszczyk",

note = "Funding Information: ✩ Both authors were partially supported by the Foundation for Polish Science. First named author was partially supported by the Israel Science Foundation, Grant 139/03. Second named author was partially supported by the Center for Advanced Studies in Mathematics of the Ben-Gurion University of the Negev. * Corresponding author. E-mail addresses: fonf@math.bgu.ac.il (V.P. Fonf), wojtaszczyk@mimuw.edu.pl (P. Wojtaszczyk).",

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doi = "10.1016/j.topol.2008.03.008",

language = "English",

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T1 - Properties of the Holmes space

AU - Fonf, V. P.

AU - Wojtaszczyk, P.

N1 - Funding Information: ✩ Both authors were partially supported by the Foundation for Polish Science. First named author was partially supported by the Israel Science Foundation, Grant 139/03. Second named author was partially supported by the Center for Advanced Studies in Mathematics of the Ben-Gurion University of the Negev. * Corresponding author. E-mail addresses: fonf@math.bgu.ac.il (V.P. Fonf), wojtaszczyk@mimuw.edu.pl (P. Wojtaszczyk).

PY - 2008/8/15

Y1 - 2008/8/15

N2 - 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.

AB - 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.

KW - Extreme points

KW - Holmes space

KW - Metric approximation property

KW - Non-complemented subspaces

KW - Urysohn space

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U2 - 10.1016/j.topol.2008.03.008

DO - 10.1016/j.topol.2008.03.008

M3 - Article

AN - SCOPUS:45849139331

SN - 0166-8641

VL - 155

SP - 1627

EP - 1633

JO - Topology and its Applications

JF - Topology and its Applications

IS - 14

ER -

Properties of the Holmes space

Abstract

Keywords

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