Geodesic
Multiplication is Discontinuous in the Hawaiian Earring Group (with the Quotient Topology)
Paul Fabel1
1 Department of Mathematics and Statistics Mississippi State University Drawer MA, Mississippi State, MS 39762, U.S.A.
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 59 (2011) no. 1, pp. 77-83

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/ba59-1-9
Keywords: natural quotient map space based loops hawaiian earring fundamental group provides naturally occuring example quotient map times fails quotient map quotient topology example shows fail topological group locally path connected

Paul Fabel 1

1 Department of Mathematics and Statistics Mississippi State University Drawer MA, Mississippi State, MS 39762, U.S.A. 
@article{10_4064_ba59_1_9,
     author = {Paul Fabel},
     title = {Multiplication is {Discontinuous} in the {Hawaiian} {Earring} {Group} (with the {Quotient} {Topology)}},
     journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
     pages = {77--83},
     publisher = {mathdoc},
     volume = {59},
     number = {1},
     year = {2011},
     doi = {10.4064/ba59-1-9},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/ba59-1-9/}
}
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
SP  - 77
EP  - 83
VL  - 59
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/ba59-1-9/
DO  - 10.4064/ba59-1-9
LA  - en
ID  - 10_4064_ba59_1_9
ER  - 
%0 Journal Article
%A Paul Fabel
%T Multiplication is Discontinuous in the Hawaiian Earring Group (with the Quotient Topology)
%J Bulletin of the Polish Academy of Sciences. Mathematics
%D 2011
%P 77-83
%V 59
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/ba59-1-9/
%R 10.4064/ba59-1-9
%G en
%F 10_4064_ba59_1_9
Paul Fabel. Multiplication is Discontinuous in the Hawaiian Earring Group (with the Quotient Topology). Bulletin of the Polish Academy of Sciences. Mathematics, Tome 59 (2011) no. 1, pp. 77-83. doi: 10.4064/ba59-1-9

Cité par Sources :