D. K. Biss (Topology and its Applications 124 (2002) 355-371)
introduced the topological fundamental group and presented some
interesting basic properties of the notion. In this article we
intend to extend the above notion to homotopy groups and try to
prove some similar basic properties of the topological homotopy
groups. We also study more on the topology of the topological
homotopy groups in order to find necessary and sufficient conditions
for which the topology is discrete. Moreover, we show that studying
topological homotopy groups may be more useful than topological
fundamental groups.
Publié le : 2008-05-15
Classification:
Topological fundamental group,
homotopy group,
$n$-semilocally simply connected,
55Q05,
55U40,
54H11,
55P35
@article{1222783092,
author = {Ghane, H. and Hamed, Z. and Mashayekhy, B. and Mirebrahimi, H.},
title = {Topological Homotopy Groups},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {15},
number = {1},
year = {2008},
pages = { 455-464},
language = {en},
url = {http://dml.mathdoc.fr/item/1222783092}
}
Ghane, H.; Hamed, Z.; Mashayekhy, B.; Mirebrahimi, H. Topological Homotopy Groups. Bull. Belg. Math. Soc. Simon Stevin, Tome 15 (2008) no. 1, pp. 455-464. http://gdmltest.u-ga.fr/item/1222783092/