Concerning connected, pseudocompact Abelian groups

Comfort, W. W.; Mill, Jan van

doi:10.1016/0166-8641(89)90086-2

Cited by 32 publications

(14 citation statements)

References 13 publications

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“…Then in 1989 Jan van Mill and I [8] solved Question I for many connected pseudocompact topological groups, and in 1992 (published in 1994) with his graduate student Helma Gladdines [6] we solved it completely for groups G which are big in the sense that |G| > c, or which are small in the sense that w(G) c.…”

Section: Questionmentioning

confidence: 98%

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Pseudocompact groups: progress and problems

Comfort

2008

Topology and its Applications

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Several months ago the speaker and Jan van Mill gave a proof of this result [W.W. Comfort, J. van Mill, Extremal pseudocompact abelian groups are compact metrizable, Abstracts Amer. Math. Soc. 27 (2006) 78 (Abstract #1014-22-958); W.W. Comfort, J. van Mill, Extremal pseudocompact abelian groups are compact metrizable, Proc. Amer. Math. Soc. 135 (2007) 4039-4044]:A pseudocompact abelian group of uncountable weight admits both a proper dense pseudocompact subgroup and a strictly larger pseudocompact group topology.This presentation will describe both the necessary new details of the argument and the historical development (useful tools, special cases). Among those who contributed essentially are: K.

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Section: Questionmentioning

confidence: 98%

“…If r 0 (G) > c, then G is neither subgroup extremal nor refinement extremal. (8) (See [29] (6.4(2)), [5] (5.7).) If G is either subgroup extremal or refinement extremal, then there is a large connected subgroup of G; indeed, for every N ∈ Λ(G) there is a connected M ∈ Λ(N ) ⊆ Λ(G).…”

Section: Questionmentioning

confidence: 99%

Pseudocompact groups: progress and problems

Comfort

2008

Topology and its Applications

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“…(b) Using (a), several workers (e.g., [4,23], [24] (2.5), [25]) made elementary cardinality observations like these, valid for infinite pseudocompact groups G.…”

Section: Pseudocompactifiability Criteria: Elementary Constraintsmentioning

confidence: 99%

Non-Abelian Pseudocompact Groups

Comfort

Remus

2016

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“…The technique used in the proof of Lemma 3.1 is well-known, and was used in many earlier results. See e.g., [3,2,12,1]. For the benefit of the reader we provide the (simple) details.…”

Section: Lemmasmentioning

confidence: 99%

“…In [2] it was shown that no pseudocompact Abelian group of cardinality greater than c is s-extremal. For partial answers in the class of connected groups, see for example [3], [12] and [1].…”

Section: Introductionmentioning

confidence: 99%