A group under \(\text{MA}_{\text{countable}}\) whose square is countably compact but whose cube is not

DOI10.1016/S0166-8641(97)00206-XzbMath0927.54039MaRDI QIDQ1292759

Artur Hideyuki Tomita

Publication date: 12 December 1999

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

zbMATH Keywords

productcountably compact

Mathematics Subject Classification ID

Structure of general topological groups (22A05) Topological groups (topological aspects) (54H11) Product spaces in general topology (54B10) Counterexamples in general topology (54G20) Continuum hypothesis and Martin's axiom (03E50)

Related Items (14)

Ultraproducts, \(p\)-limits and antichains on the Comfort group order ⋮ Varieties generated by countably compact Abelian groups ⋮ Countably compact groups from a selective ultrafilter ⋮ Convergent sequences in topological groups ⋮ A van Douwen-like ZFC theorem for small powers of countably compact groups without non-trivial convergent sequences ⋮ Almost \(p\)-compact groups ⋮ Open problems in topology. ⋮ Countably compact groups without non-trivial convergent sequences ⋮ Countable compactness and finite powers of topological groups without convergent sequences ⋮ Open problems in topology, seventh status report ⋮ Finite powers of selectively pseudocompact groups ⋮ Square of countably compact groups without non-trivial convergent sequences ⋮ Provisional solution to a Comfort--van Mill problem ⋮ Independent group topologies on abelian groups

Cites Work

• Set theory. An introduction to independence proofs
• Pseudocompactness and uniform continuity in topological groups
• Locally precompact groups: (Local) realcompactness and connectedness
• The Product of Two Countably Compact Topological Groups
• A Countably Compact Topological Group H Such that H × H is not Countably Compact
• A separable normal topological group need not be Lindelöf
• The Wallace Problem: A Counterexample from Ma_Countableand_p-Compactness
• An answer to A.D.Wallace’s question about countably compact cancellative semigroups
• The structure of topological semigroups
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