Hausdorff properties of topological algebras

被引：5

作者：

Kearnes, K ^{[1
]}

Sequeira, L

机构：

[1] Univ Colorado, Dept Math, Boulder, CO 80309 USA

[2] Univ Lisbon, Fac Ciencias, Dept Matemat, P-1749016 Lisbon, Portugal

[3] Univ Lisbon, Ctr Algebra, P-1649003 Lisbon, Portugal

来源：

ALGEBRA UNIVERSALIS | 2002年 / 47卷 / 04期

基金：

美国国家科学基金会;

关键词：

topological algebra; separation axioms; ultraproduct topology; Maltsev condition; k-permutable variety; congruence modular variety;

D O I：

10.1007/s00012-002-8194-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let P be a property of topological spaces. Let [P] be the class of all varieties V having the property that any topological algebra in V has underlying space satisfying property P. We show that if P is preserved by finite products, and if -P is preserved by ultraproducts, then [P] is a class of varieties that is definable by a Maltsev condition. The property that all T-0 topological algebras in V are j-step Hausdorff (H-j) is preserved by finite products, and its negation is preserved by ultraproducts. We partially characterize the Maltsev condition associated to T-0 double right arrow H-j by showing that this topological implication holds in every (2(j) + 1)-permutable variety, but not in every (2j + 2)-permutable variety. Finally, we show that the topological implication T-0 double right arrow T-2 holds in every k-permutable, congruence modular variety.

引用

页码：343 / 366

页数：24