TY - JOUR

T1 - Products of topological groups in which all closed subgroups are separable

AU - Leiderman, Arkady G.

AU - Tkachenko, Mikhail G.

N1 - Funding Information:
The authors have been supported by CONACyT of Mexico, grant number CB-2012-01 178103.
Publisher Copyright:
© 2018 Elsevier B.V.

PY - 2018/6/1

Y1 - 2018/6/1

N2 - We prove that if H is a topological group such that all closed subgroups of H are separable, then the product G×H has the same property for every separable compact group G. Let c be the cardinality of the continuum. Assuming 2ω1 =c, we show that there exist: • pseudocompact topological abelian groups G and H such that all closed subgroups of G and H are separable, but the product G×H contains a closed non-separable σ-compact subgroup;• pseudocomplete locally convex vector spaces K and L such that all closed vector subspaces of K and L are separable, but the product K×L contains a closed non-separable σ-compact vector subspace.

AB - We prove that if H is a topological group such that all closed subgroups of H are separable, then the product G×H has the same property for every separable compact group G. Let c be the cardinality of the continuum. Assuming 2ω1 =c, we show that there exist: • pseudocompact topological abelian groups G and H such that all closed subgroups of G and H are separable, but the product G×H contains a closed non-separable σ-compact subgroup;• pseudocomplete locally convex vector spaces K and L such that all closed vector subspaces of K and L are separable, but the product K×L contains a closed non-separable σ-compact vector subspace.

KW - Closed subgroup

KW - Locally convex space

KW - Pseudocompact

KW - Pseudocomplete

KW - Separable

KW - Topological group

UR - http://www.scopus.com/inward/record.url?scp=85044957534&partnerID=8YFLogxK

U2 - 10.1016/j.topol.2018.03.022

DO - 10.1016/j.topol.2018.03.022

M3 - Article

AN - SCOPUS:85044957534

SN - 0166-8641

VL - 241

SP - 89

EP - 101

JO - Topology and its Applications

JF - Topology and its Applications

ER -