JOURNAL ARTICLE

Varieties generated by countably compact Abelian groups

Dikran DikranjanMikhail Tkachenko

Year: 2002 Journal:   Proceedings of the American Mathematical Society Vol: 130 (8)Pages: 2487-2496   Publisher: American Mathematical Society

Abstract

We prove under the assumption of Martin's Axiom that every precompact Abelian group of size $\leq 2^{\aleph _0}$ belongs to the smallest class of groups that contains all Abelian countably compact groups and is closed under direct products, taking closed subgroups and continuous isomorphic images.

Keywords:
Abelian group Mathematics Axiom Class (philosophy) Countable set Pure mathematics Rank of an abelian group Elementary abelian group Group (periodic table) Axiom of choice Locally compact space Aleph Discrete mathematics Computer science Set theory Set (abstract data type) Physics Geometry Artificial intelligence

Metrics

9
Cited By
2.21
FWCI (Field Weighted Citation Impact)
31
Refs
0.81
Citation Normalized Percentile
Is in top 1%
Is in top 10%

Citation History

Topics

Advanced Topology and Set Theory
Physical Sciences →  Mathematics →  Geometry and Topology
Rings, Modules, and Algebras
Physical Sciences →  Mathematics →  Algebra and Number Theory
Computability, Logic, AI Algorithms
Physical Sciences →  Computer Science →  Computational Theory and Mathematics

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