Homotopy groups
are introduced by Hurewicz in 1935. Although the
definition is fairly simple, it is very hard to
determine homotopy groups in general.
Homotopy groups are algebraic invariants with
emphasis on spheres and balls, and they are
fundamental and important in the world of
CWcomplexes
. For
exotic spaces
which do not have the homotopy type of CWcomplexes,
however, we need an alternative framework to work
with. One of such examples is the Steenrod homotopy
theory
[
Mel
]
.
Some people think that it is unnatural to restrict
our attentions to continuous maps and study
spaces of notnecessarilycontinous maps
.
