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

Tom 59 / 2011

Paul Fabel Bulletin Polish Acad. Sci. Math. 59 (2011), 77-83 MSC: Primary 54G20; Secondary 54B15. DOI: 10.4064/ba59-1-9

Streszczenie

The natural quotient map $q$ from the space of based loops in the Hawaiian earring onto the fundamental group provides a naturally occuring example of a quotient map such that $q\times q$ fails to be a quotient map. With the quotient topology, this example shows $\pi _{1}(X,p)$ can fail to be a topological group if $X$ is locally path connected.

Autorzy

  • Paul FabelDepartment of Mathematics and Statistics
    Mississippi State University
    Drawer MA, Mississippi State, MS 39762, U.S.A.
    e-mail

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