Topological gyrogroups: generalization of topological groups

DOI10.1016/j.topol.2017.04.004zbMath1382.22008OpenAlexW2606307651MaRDI QIDQ526886

Watchareepan Atiponrat

Publication date: 15 May 2017

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

Full work available at URL: https://doi.org/10.1016/j.topol.2017.04.004

zbMATH Keywords

topological loopstopological monoidstopological quasigroups

Mathematics Subject Classification ID

Topological groups (topological aspects) (54H11) Loops, quasigroups (20N05) Other topological algebraic systems and their representations (22A30)

Related Items (22)

Quotient with respect to admissible \(L\)-subgyrogroups ⋮ Cardinal invariants in the quotient spaces of weakly topological groups ⋮ Geometry of gyrogroups via Klein's approach ⋮ Some results on rectifiable spaces ⋮ Topological gyrogroups with Fréchet-Urysohn property and \(\omega^{\omega}\)-base ⋮ Strongly topological gyrogroups with remainders close to metrizable ⋮ Fuzzy gyronorms on gyrogroups ⋮ The Hartman-Mycielski construction in topological gyrogroups ⋮ The first-countability in the quotient spaces of topological gyrogroups ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ The first-countability of paratopological left-loops ⋮ On Metric Structures of Normed Gyrogroups ⋮ Uniformities on strongly topological gyrogroups ⋮ A note on paratopological loops ⋮ Complete regularity of paratopological gyrogroups ⋮ Embedding of locally compact Hausdorff topological gyrogroups in topological groups ⋮ A note on (strongly) topological gyrogroups ⋮ On paratopological gyrogroups ⋮ Feathered gyrogroups and gyrogroups with countable pseudocharacter ⋮ Extensions of some topological properties in topological gyrogroups

Cites Work

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• Gyrogroup actions: a generalization of group actions
• On the notion of gyrogroup
• Introduction to topological groups
• Isomorphism theorems for gyrogroups and L-subgyrogroups.
• Induced topologies for quasigroups and loops
• Topological quasi-group shifts
• Topological Right Gyrogroups and Gyrotransversals
• Each regular paratopological group is completely regular
• TOPOLOGICAL QUASIGROUPS
• The Algebra of Gyrogroups: Cayley’s Theorem, Lagrange’s Theorem, and Isomorphism Theorems
• Lagrange's Theorem for Gyrogroups and the Cauchy Property
• Topological Loops With Invariant Uniformities
• Contributions to the Theory of Loops

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