Open AccessWeakly metrizable pseudocompact groups
Author(s) -
Dikran Dikranjan,
Anna Giordano Bruno,
Chiara Milan
Publication year - 2006
Publication title -
applied general topology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.638
H-Index - 13
eISSN - 1989-4147
pISSN - 1576-9402
DOI - 10.4995/agt.2006.1930
Subject(s) - metrization theorem , mathematics , modulo , abelian group , mathematical proof , group (periodic table) , pure mathematics , social connectedness , combinatorics , discrete mathematics , mathematical analysis , physics , geometry , psychology , quantum mechanics , separable space , psychotherapist
We study various weaker versions of metrizability for pseudocompact abelian groups G: singularity (G possesses a compact metrizable subgroup of the form mG, m>0), almost connectedness (G is metrizable modulo the connected component) and various versions of extremality in the sense of Comfort and co-authors (s-extremal, if G has no proper dense pseudocompact subgroups, r-extremal, if G admits no proper pseudocompact refinement). We introduce also weaklyextremal pseudocompact groups (weakening simultaneously s-extremal and r-extremal). It turns out that this “symmetric” version of ex-tremality has nice properties that restore the symmetry, to a certain extent, in the theory of extremal pseudocompact groups obtaining simpler uniform proofs of most of the known results. We characterize doubly extremal pseudocompact groups within the class of s-extremal pseudocompact groups. We give also a criterion for r-extremality for connected pseudocompact groups