Multiplication is Discontinuous in the Hawaiian Earring Group (with the Quotient Topology)

DOI10.4064/ba59-1-9zbMath1229.54046arXiv0909.3086OpenAlexW2962916289MaRDI QIDQ3008469

Paul Fabel

Publication date: 15 June 2011

Published in: Bulletin of the Polish Academy of Sciences Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0909.3086

zbMATH Keywords

topological groupHawaiian earringquotient of products

Mathematics Subject Classification ID

Topological groups (topological aspects) (54H11) Quotient spaces, decompositions in general topology (54B15) Homotopy groups (55Q99)

Related Items (16)

On the discontinuity of the \(\pi_1\)-action ⋮ A new topology on the universal path space ⋮ A core-free semicovering of the Hawaiian earring ⋮ On maps with continuous path lifting ⋮ On topological shape homotopy groups ⋮ A natural pseudometric on homotopy groups of metric spaces ⋮ The topological fundamental group and free topological groups ⋮ The comparison of topologies related to various concepts of generalized covering spaces ⋮ Topological coarse shape homotopy groups ⋮ On topological homotopy groups and relation to Hawaiian groups ⋮ On fundamental groups with the quotient topology ⋮ Some results in quasitopological homotopy groups ⋮ Topological Realisations of Absolute Galois Groups ⋮ On first countable quasitopological homotopy groups ⋮ Eilenberg-Mac Lane spaces for topological groups ⋮ On topologized fundamental groups with small loop transfer viewpoints

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