Countably compact topological group topologies on free Abelian groups from selective ultrafilters

DOI10.1016/J.TOPOL.2006.03.028zbMath1116.54004OpenAlexW2074624343MaRDI QIDQ876543

Artur Hideyuki Tomita, Roberto E. Madariaga-Garcia

Publication date: 18 April 2007

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.topol.2006.03.028

zbMATH Keywords

selective ultrafiltercontinuum hypothesiscountably compact groupfree Abelian groupMartin's Axiomgroups without non-trivial convergent sequencestotal failure of Martin's AxiomWallace semigroup

Mathematics Subject Classification ID

Structure of general topological groups (22A05) Topological groups (topological aspects) (54H11) Noncompact covering properties (paracompact, Lindelöf, etc.) (54D20) Counterexamples in general topology (54G20) Applications of set theory (03E75) Structure of topological semigroups (22A15) Consistency and independence results in general topology (54A35)

Related Items (17)

Some pseudocompact-like properties in certain topological groups ⋮ Convergent sequences in topological groups ⋮ Transversal, \(T_{1}\)-independent, and \(T_{1}\)-complementary topologies ⋮ Positive answers to Koch's problem in special cases ⋮ A van Douwen-like ZFC theorem for small powers of countably compact groups without non-trivial convergent sequences ⋮ Embedding the bicyclic semigroup into countably compact topological semigroups ⋮ A countably compact topological group with the non-countably pracompact square ⋮ Countably compact group topologies on arbitrarily large free abelian groups ⋮ A countably compact free Abelian group of size continuum that admits a non-trivial convergent sequence ⋮ A group topology on the free abelian group of cardinality \(\mathfrak{c}\) that makes its finite powers countably compact ⋮ On feebly compact paratopological groups ⋮ Suitable sets for paratopological groups ⋮ Forcing a classification of non-torsion abelian groups of size at most \(2^{\mathfrak{c}}\) with non-trivial convergent sequences ⋮ Algebraic structure of countably compact non-torsion abelian groups of size continuum from selective ultrafilters ⋮ Abelian torsion groups with a countably compact group topology ⋮ Countably compact group topologies on non-torsion abelian groups of size continuum with non-trivial convergent sequences ⋮ The continuity of the inversion and the structure of maximal subgroups in countably compact topological semigroups

Cites Work

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• Forcing hereditarily separable compact-like group topologies on Abelian groups
• Sacks forcing and the total failure of Martin's axiom
• Set theory. An introduction to independence proofs
• Independent group topologies on abelian groups
• Ultraproducts, \(p\)-limits and antichains on the Comfort group order
• Locally precompact groups: (Local) realcompactness and connectedness
• Algebraic structure of pseudocompact groups
• The Weight of a Pseudocompact (Homogeneous) Space Whose Cardinality Has Countable Cofinality
• The Product of Two Countably Compact Topological Groups
• A Countably Compact Topological Group H Such that H × H is not Countably Compact
• The Wallace Problem: A Counterexample from Ma_Countableand_p-Compactness
• Algebraic structure of small countably compact Abelian groups
• A countably compact free Abelian group whose size has countable cofinality
• Two countably compact topological groups: One of size $\aleph _\omega $ and the other of weight $\aleph _\omega $ without non-trivial convergent sequences
• Countably compact groups from a selective ultrafilter
• An answer to A.D.Wallace’s question about countably compact cancellative semigroups
• A new kind of compactness for topological spaces
• The Rudin-Keisler Ordering of P-Points
• A solution to Comfort's question on the countable compactness of powers of a topological group

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