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

• Autorzy: Paul Fabel
• Języki publikacji: EN

Abstrakty

EN

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 × q fails to be a quotient map. With the quotient topology, this example shows π₁(X,p) can fail to be a topological group if X is locally path connected.

Kategorie tematyczne

• 54G20: Counterexamples
• 54B15: Quotient spaces, decompositions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2011
• Tom: 59
• Numer: 1
• Strony: 77-83

Daty

wydano

2011

Twórcy

autor

Paul Fabel

• Department of Mathematics and Statistics, Mississippi State University, Drawer MA, Mississippi State, MS 39762, U.S.A.

Identyfikatory

DOI

10.4064/ba59-1-9