### Impacto

Nhu, Nguyen Tho and Rodríguez Sanjurjo, José Manuel and Van An, Tran
(1997)
*The AR-property for Roberts' example of a compact convex set with no extreme points .2. Application to the example.*
Proceedings of the American Mathematical Society, 125
(10).
pp. 3089-3098.
ISSN 0002-9939

PDF
Restringido a Repository staff only hasta 31 December 2020. 222kB |

Official URL: http://www.ams.org/journals/proc/1997-125-10/S0002-9939-97-04021-5/S0002-9939-97-04021-5.pdf

## Abstract

In this second part of our paper, we apply the result of Part 1 to show that the compact convex set with no extreme points, constructed by Roberts (1977), is an AR.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | Convex set, linear metric space, extreme point, absolute retract |

Subjects: | Sciences > Mathematics > Geometry Sciences > Mathematics > Topology |

ID Code: | 16904 |

References: | C. Bessaga and T. Dobrowolski, Some open problems on the border of infinite dimensional topology and functional analysis, Proceedings of the international conference on geometric topology, PWN, Warszawa 1980. D. Curtis, T. Dobrowolski and J. Mogilski, Some applications of the topological characterizations of the sigma-compact spaces 2 f nad , Trans. Amer. Math. Soc. 284(1984), 837{847 T. Dobrowolski and J. Mogilski, Problems on topological classification of incomplete metric spaces, Open problems in topology, J. van Mill and G. M. Reed (Editors) Elsevier Science Publishers B. V. North-Holand 1990. R. Geoghegan, Open problems in infinite dimensional topology, Topology Proceedings, 4(1979), 287{330. V. Klee, Shrinkable neighbourhoods in Hausdor linear spaces, Math. Ann. 141(1960), 281{285. V. Klee, Leray-Schauder theory without local convexity, Math. Ann. 141(1960), 286{296. M. G. Krein and D. P. Milman, On extreme points of regular convex sets, Studia Math. 9(1940), 133{138. N. J. Kalton and N. T. Peck, A re-examination of Roberts' example of a compact convex set with no extreme points, Math. Ann. 253(1980), 89{101. N. J. Kalton, N. T. Peck and J. W. Roberts, An F-space sampler, London Math. Soc. Lecture Note Series 89(1984). Nguyen To Nhu, Investigating the ANR-property of metric spaces, Fund. Math. 124(1984), 243{254; Correction, Fund. Math. 141(1992), 297. Nguyen To Nhu, The infinite dimensional approximation property and the AR-property in needle point spaces, J. London Math. Soc. (to appear). Nguyen To Nhu and Katsuro Sakai, The compact neighborhood extension property and the local equi-connectedness, Proc. Amer. Math. Soc. 121(1994), 259{265. Nguyen To Nhu and Le Hoang Tri, Every needle point space contains a compact convex AR-set with no extreme points, Proc. Amer. Math. Soc. 120(1994), 1261{1265 Nguyen To Nhu and Le Hoang Tri, No Roberts space is a counter-example to Schauder's conjecture, Topology, 33(1994), 371{378. |

Deposited On: | 26 Oct 2012 10:44 |

Last Modified: | 07 Feb 2014 09:38 |

Repository Staff Only: item control page