Free topological groups

Thomas, Barbara V. Smith

doi:10.1016/0016-660x(74)90005-1

Cited by 39 publications

(5 citation statements)

References 11 publications

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“…It is worthwhile to note that connected torsion groups of bounded order, as hypothesized in Theorem 3.25, do exist. Here we give two quite different proofs that for 0 < n < ω there is a nontrivial connected torsion group of exponent n. Of these (A), as remarked by the referee, uses the construction given in Theorem 3.20; while (B), drawing freely on the expositions [37] and [2](2.3-2.4), derives from the "free topological group" constructions first given by Markov [25], [26] and Graev [21].…”

Section: Proofmentioning

confidence: 99%

Topologies on Abelian Groups

Zelenyuk¹,

Протасов²

1991

Math. USSR Izv.

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A Hausdorff topological group G = (G, T ) has the small subgroup generating property (briefly: has the SSGP property, or is an SSGP group) if for each neighborhood U of 1G there is a family H of subgroups of G such that H ⊆ U and H is dense in G. The class of SSGP groups is defined and investigated with respect to the properties usually studied by topologists (products, quotients, passage to dense subgroups, and the like), and with respect to the familiar class of minimally almost periodic groups (the m.a.p. groups). Additional classes SSGP(n) for n < ω (with SSGP(1) = SSGP) are defined and investigated, and the class-theoretic inclusionsare established and shown proper. In passing the authors also establish the presence of SSGP(1) or SSGP(2) in many of the early examples in the literature of abelian m.a.p. groups.2010 MSC: Primary 54H11; Secondary 22A05.

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Section: Proofmentioning

confidence: 99%

Topologies on Abelian Groups

Zelenyuk¹,

Протасов²

1991

Math. USSR Izv.

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“…Alternate latter-day constructions abound, some achieved independently of [82][83][84][85] and some based on those works, some with algebraic emphasis [86,87], [2] (8.8,8.9), [24] (2.3-2.5), some topological [88][89][90], some functorial or categorical [91]. See [92] ( §4) for a comprehensive introduction to the groups FX and FAX, and see [62] for generalizations to "free P-spaces" for some other classes P.…”

Section: Characterizations Of Fx and Faxmentioning

confidence: 99%

Non-Abelian Pseudocompact Groups

Comfort

Remus

2016

Axioms

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“…These two facts imply that L(Y ) can be identified with L(Y, X). Since Y is closed in X we can repeat word for word the proof of [16,Proposition 3.8]…”

Section: Question 23mentioning

confidence: 99%