Continuous Duality of Limits and Colimits of Topological Abelian Groups

被引：0

作者：

R. Beattie

H.-P. Butzmann

机构：

[1] Mount Allison University,Department of Mathematics and Computer Science

[2] Universität Mannheim,Fakultät für Mathematik und Informatik

来源：

Applied Categorical Structures | 2008年 / 16卷

关键词：

Continuous convergence; Duality of topological groups; Limits; Colimits; Pontryagin duality; 43A40; 54A20; 18A30;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

In the category Cgp of convergence groups, the continuous dual Γc( ·) is a left adjoint and takes colimits to limits in Cgp. In general, limits are not taken to colimits. In this paper we show that, if we restrict ourselves to limits of topological groups, then reduced projective limits are carried to inductive limits in Cgp. As a consequence of this we show that the inductive limit in Cgp of locally compact topological groups is reflexive if it is separated.

引用

页码：535 / 549

页数：14

共 50 条

[1] Continuous duality of limits and colimits of topological Abelian groups
Beattie, R.
Butzmann, H. -P.
[J]. APPLIED CATEGORICAL STRUCTURES, 2008, 16 (04) : 535 - 549
[2] CONTINUOUS CONVERGENCE AND DUALITY OF LIMITS OF TOPOLOGICAL ABELIAN GROUPS
Ardanza-Trevijano, S.
Chasco, M. J.
[J]. BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA, 2007, 13 (01): : 15 - 23
[3] The Pontryagin duality of sequential limits of topological Abelian groups
Ardanza-Trevijano, S
Chasco, MJ
[J]. JOURNAL OF PURE AND APPLIED ALGEBRA, 2005, 202 (1-3) : 11 - 21
[4] Pontryagin duality for topological Abelian groups
Hernández, S
[J]. MATHEMATISCHE ZEITSCHRIFT, 2001, 238 (03) : 493 - 503
[5] Pontryagin duality for topological Abelian groups
Salvador Hernández
[J]. Mathematische Zeitschrift, 2001, 238 : 493 - 503
[6] Colimits of abelian groups
Okay, Cihan
[J]. JOURNAL OF ALGEBRA, 2015, 443 : 1 - 12
[7] Long colimits of topological groups I: Continuous maps and homeomorphisms
Dahmen, Rafael
Lukacs, Gabor
[J]. TOPOLOGY AND ITS APPLICATIONS, 2020, 270
[8] Tensor products of topological abelian groups and Pontryagin duality
Ferrer, Maria V.
Hernandez-Arzusa, Julio
Hernandez, Salvador
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2024, 536 (02)
[9] THE FREE TOPOLOGICAL ABELIAN-GROUPS AND PONTRYAGIN DUALITY
PESTOV, VG
[J]. VESTNIK MOSKOVSKOGO UNIVERSITETA SERIYA 1 MATEMATIKA MEKHANIKA, 1986, (01): : 3 - 5
[10] Duality properties of bounded torsion topological abelian groups
Chasco, M. J.
Dominguez, X.
Tkachenko, M.
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2017, 448 (02) : 968 - 981

← 1 2 3 4 5 →