Unconditionally tau-Closed and tau-Algebraic Sets in Groups

Simple item page
dc.creatorSipacheva, Ol'ga V.
dc.date2007-03-13
dc.date2007-06-14
dc.date.accessioned2026-07-07T08:09:57Z
dc.date.available2026-07-07T08:09:57Z
dc.descriptionFamilies of unconditionally $τ$-closed and $τ$-algebraic sets in a group are defined, which are natural generalizations of unconditionally closed and algebraic sets defined by Markov. A sufficient condition for the coincidence of these families is found. In particular, it is proved that these families coincide in any group of cardinality at most $τ$. This result generalizes both Markov's theorem on the coincidence of unconditionally closed and algebraic sets in a countable group (as is known, they may be different in an uncountable group) and Podewski's theorem on the topologizablity of any ungebunden group.
dc.descriptionVersion 2: A mistake is corrected. The main result is changed accordingly Version 3: Minor changes are made
dc.identifierhttps://arxiv.org/abs/math/0703397
dc.identifierhttp://arxiv.org/abs/math/0703397
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/131702
dc.subjectGroup Theory
dc.subjectGeneral Topology
dc.subject54H11, 22A05
dc.titleUnconditionally tau-Closed and tau-Algebraic Sets in Groups
dc.typetext

Files

Collections

arXiv