Menger (Nobeling) manifolds versus Hilbert cube (space) manifolds - A categorical comparison

被引：1

作者：

Chigogidze, A

Fedorchuk, VV

机构：

[1] Univ Saskatchewan, Dept Math & Stat, Saskatoon, SK S7N 5E6, Canada

[2] Moscow State Univ, Fac Mech & Math, Chair Gen Topol & Geometry, Moscow 119899, Russia

来源：

MONATSHEFTE FUR MATHEMATIK | 2000年 / 130卷 / 02期

关键词：

Menger manifold; Hilbert cube manifold; n-homotopy; Postnikov functor;

D O I：

10.1007/s006050070039

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that the n-homotopy category MENG(n) of connected (n + 1)-dimensional Menger manifolds is isomorphic to the homotopy category HILBCn of connected Hilbert cube manifolds whose k-dimensional homotopy groups are trivial for each k greater than or equal to n + 1 . 1991 Mathematics Subject Classification: 57Q05; 55P65.

引用

页码：89 / 97

页数：9

共 49 条

[1] Menger (Nöbeling) Manifolds versus Hilbert Cube (Space) Manifolds – A Categorical Comparison
Alex Chigogidze
V. V. Fedorchuk
Monatshefte für Mathematik, 2000, 130 : 89 - 97
[2] HILBERT CUBE MANIFOLDS
CHAPMAN, TA
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1970, 76 (06) : 1326 - &
[3] STRUCTURE OF HILBERT CUBE MANIFOLDS
CHAPMAN, TA
COMPOSITIO MATHEMATICA, 1972, 24 (03) : 329 - &
[4] CONCORDANCES OF HILBERT CUBE MANIFOLDS
CHAPMAN, TA
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1976, 219 (MAY) : 253 - 268
[5] HOMEOMORPHISMS OF HILBERT CUBE MANIFOLDS
CHAPMAN, TA
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 182 (AUG) : 227 - 239
[6] CONTRACTIBLE HILBERT CUBE MANIFOLDS
CHAPMAN, TA
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 35 (01) : 254 - +
[7] HILBERT CUBE MANIFOLDS OF MAPS
GEOGHEGA.R
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1974, 21 (05): : A503 - A503
[8] HOMEOMORPHISM GROUPS OF COMPACT HILBERT CUBE MANIFOLDS WHICH ARE MANIFOLDS
TORUNCZYK, H
BULLETIN DE L ACADEMIE POLONAISE DES SCIENCES-SERIE DES SCIENCES MATHEMATIQUES ASTRONOMIQUES ET PHYSIQUES, 1977, 25 (04): : 401 - 408
[9] CONCORDANCES OF NONCOMPACT HILBERT CUBE MANIFOLDS
CHAPMAN, TA
PACIFIC JOURNAL OF MATHEMATICS, 1976, 63 (01) : 89 - 124
[10] TRIANGULATION AND CLASSIFICATION OF HILBERT CUBE MANIFOLDS
CHAPMAN, TA
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 19 (07): : A810 - A810

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