ALL libraries (COBIB.SI union bibliographic/catalogue database)
13.
Metrization criteria for compact groups in terms of their dense subgroups
Dikranjan, Dikran N., 1950- ; Shakhmatov, Dmitri
According to Comfort, Raczkowski and Trigos-Arrieta, a dense subgroup ▫$D$▫ of acompact abelian group ▫$G$▫ determines ▫$G$▫ if the restriction homomorphism ▫$\widehat{G} \to \widehat{D}$▫ of the ...dual groups is a topological isomorphism. We introduce four conditions on ▫$D$▫ that are necessary for it to determine ▫$G$▫ and we resolve the following question: If one of these conditions holds forevery dense (or ▫$G_\delta$▫-dense) subgroup ▫$D$▫ of ▫$G$▫, must ▫$G$▫ be metrizable? In particular, we prove (in ZFC) that a compact abelian group determined by all its ▫$G_\delta$▫-dense subgroups is metrizable, thereby resolving a question of Hernández, Macario and Trigos-Arrieta. (Under the additional assumption of the Continuum Hypothesis CH, the same statement was proved recently by Bruguera, Chasco, Domínguez, Tkachenko and Trigos-Arrieta.) As a tool, we develop a machinery for building ▫$G_\delta$▫-dense subgroups without uncountable compact subsets in compact groups of weight ▫$\omega_1$▫ (in ZFC). The construction is delicate, as these subgroups must have non-trivial convergent sequences in some models of ZFC.
It was not necessary to add the material to the shelf.
Bibliographic material was successfully added on shelf.
Adding bibliographical material on shelf was not successful.
Material is already on the shelf.
Permalink
URL:
Impact factor
Access to the JCR database is permitted only to users from Slovenia. Your current IP address is not on the list of IP addresses with access permission, and authentication with the relevant AAI accout is required.
Year
Impact factor
Edition
Category
Classification
JCR
SNIP
JCR
SNIP
JCR
SNIP
JCR
SNIP
Impact factor
Select the library membership card:
DRS,
in which the journal is indexed
Database name
Field
Year
Links to authors' personal bibliographies
Links to information on researchers in the SICRIS system
Subject headings in COBISS General List of Subject Headings
Select pickup location
The material from the parent unit is free. If the material is delivered to the pickup location from another unit, the library may charge you for this service.
