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  • Essential subgroups of topological groups
    Boschi, Elena ; Dikranjan, Dikran N., 1950-
    We study the class ▫$W$▫ of Hausdorff topological groups ▫$G$▫ for which the following two cardinal invariants coincide: ▫$$ES(G) = \min\{|H|:H \le G \; \text{dense and essential}\}$$▫ ▫$$TD(G) = ... \min \{|H|:H \le G \; \text{totally dense}\}.$$▫ We prove that ▫$W$▫ contains the following classes: locally compact Abelian groups, compact connected groups, countably compact totally disconnected abelian groups, topologically simple groups, locally compact Abelian groups when endowed with their Bohr topology, totally minimal Abelian groups and free Abelian topological groups. For all these classes we are also able to give an explicit computation of the common value of ▫$ES$▫ and ▫$TD$▫.
    Vir: Communications in algebra. - ISSN 0092-7872 (Vol. 28, no. 10, 2000, str. 4941-4970)
    Vrsta gradiva - članek, sestavni del
    Leto - 2000
    Jezik - angleški
    COBISS.SI-ID - 16247897

    Povezava(-e):

    http://dx.doi.org/10.1080/00927870008827133

vir: Communications in algebra. - ISSN 0092-7872 (Vol. 28, no. 10, 2000, str. 4941-4970)
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