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

@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 -