Algebra, Logic and Topology

 

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Author(s)
Francis Borceux; Maria Manuel Clementino;

Title
Topological semi-abelian algebras

Abstract
Given an algebraic theory T whose category of models is semi-abelian, we study the category Top^T of topological models of T and generalize to it most classical results on topological groups. In particular Top^T is homological, which includes Barr regularity and forces the Mal'cev property. Every open subalgebra is closed and every quotient map is open. We devote special attention to the Hausdorff, compact, locally compact, connected, totally disconnected and profinite T-algebras.

Journal
Advances in Mathematics

Volume
190

Year
2005

Issue
1

Page(s)
425-453

 
     
 

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