Compact-Like Totally Dense Subgroups of Compact Groups

DOI10.2307/2159637zbMath0781.54018OpenAlexW4241672769MaRDI QIDQ3991951

Dikran Dikranjan, Dmitrij B. Shakhmatov

Publication date: 28 June 1992

Full work available at URL: https://doi.org/10.2307/2159637

zbMATH Keywords

compact groupcountably compact grouppseudocompact groupLusin's hypothesistotally minimal group\(G_ \delta\)-subgrouptotally dense subgroup

Mathematics Subject Classification ID

Topological groups (topological aspects) (54H11) ``(P)-minimal and ``(P)-closed spaces (54D25) Compact groups (22C05) Consistency and independence results in general topology (54A35)

Related Items (16)

Countably compact groups having minimal infinite powers ⋮ Quotients of locally minimal groups ⋮ The gentle, generous giant tampering with dense subgroups of topological groups ⋮ Non-abelian pseudocompact groups ⋮ Abelian group theory in Italy. ⋮ Characterizing Lie groups by controlling their zero-dimensional subgroups ⋮ Closures of Weakened Analytic Groups ⋮ w-divisible groups ⋮ Dense minimal pseudocompact subgroups of compact Abelian groups ⋮ Zero-Dimensionality of Some Pseudocompact Groups ⋮ Sequentially complete groups: Dimension and minimality ⋮ Pseudocompact totally dense subgroups ⋮ Cardinal invariants and convergence properties of locally minimal groups ⋮ Recent advances in minimal topological groups ⋮ Compactness and connectedness in topological groups ⋮ Boundedness in \({\mathcal C}_p(X,Y)\) and equicontinuity

Cites Work

• Cardinality constraints for pseudocompact and for totally dense subgroups of compact topological groups
• Set theory. An introduction to independence proofs
• Pseudocompact group topologies and totally dense subgroups
• Pseudocompactness and uniform continuity in topological groups
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