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Resolvability in Topology and in Topological Groups
Author(s) -
COMFORT W. W.,
MASAVEU OSCAR,
ZHOU HAO
Publication year - 1995
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1111/j.1749-6632.1995.tb55890.x
Subject(s) - topological group , mathematics , group (periodic table) , abelian group , bounded function , hausdorff space , locally compact space , uncountable set , topology (electrical circuits) , combinatorics , connected space , discrete mathematics , topological space , physics , countable set , mathematical analysis , quantum mechanics
A space is resolvable if it contains complementary dense subsets. Among the results proved here, are these. Let G i (1 ≤ i ≤ 6) be nondiscrete Hausdorff topological groups with G i Abelian (1 ≤ i ≤ 4), G 3 locally bounded, G 4 a Baire group, and G 5 totally bounded and uncountable. Then G 1 × G 2 , G 3 , G 4 , G 5 , and G 6 × G 6 are resolvable.