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Identifying and distinguishing various varieties of abelian topological groups

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McPhail C., Morris S.

Instytut Matematyczny Polskiej Akademii Nauk

A variety of topological groups is a class of (not necessarily Hausdorff) topological groups closed under the operations of forming subgroups, quotient groups and arbitrary products. The variety of topological groups generated by a class of topological groups is the smallest variety containing the class. In this paper methods are presented to distinguish a number of significant varieties of abelian topological groups, including the varieties generated by (i) the class of all locally compact abelian groups; (ii) the class of all $k_{ω}$-groups; (iii) the class of all σ-compact groups; and (iv) the free abelian topological group on [0,1]. In all cases, hierarchical containments are determined.

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1 McPhail C.

1 Morris S.

1 2008

Wyniki wyszukiwania

Identifying and distinguishing various varieties of abelian topological groups