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

Paul Fabel. "Multiplication is Discontinuous in the Hawaiian Earring Group (with the Quotient Topology)." Bulletin of the Polish Academy of Sciences. Mathematics 59.1 (2011): 77-83. <http://eudml.org/doc/281130>.

@article{PaulFabel2011,
abstract = {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.},
author = {Paul Fabel},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {topological group; quotient of products; Hawaiian earring},
language = {eng},
number = {1},
pages = {77-83},
title = {Multiplication is Discontinuous in the Hawaiian Earring Group (with the Quotient Topology)},
url = {http://eudml.org/doc/281130},
volume = {59},
year = {2011},
}

TY - JOUR
AU - Paul Fabel
TI - Multiplication is Discontinuous in the Hawaiian Earring Group (with the Quotient Topology)
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2011
VL - 59
IS - 1
SP - 77
EP - 83
AB - 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.
LA - eng
KW - topological group; quotient of products; Hawaiian earring
UR - http://eudml.org/doc/281130
ER -