- #1
nughret
- 45
- 0
I am trying to show that the space Cone(L(X,x)) is homeomorphic to P(X,x)
where L(X,x) = {loops in X base point x} and
P(X,x) = {paths in X base point x}
I firstly considered (L(X,x) x I) and tried to find a surjective map to P(X,x) that would quotient out right but i couldn't seem to find it. For example i considered
(l,t) -> p where p is the path such that p(1)=l(t) and they agree naturally before
i.e. F((l,t))(s) = l(ts)
I was wondering if anyone could point me roughly the right way or just chip in with their own thoughts
where L(X,x) = {loops in X base point x} and
P(X,x) = {paths in X base point x}
I firstly considered (L(X,x) x I) and tried to find a surjective map to P(X,x) that would quotient out right but i couldn't seem to find it. For example i considered
(l,t) -> p where p is the path such that p(1)=l(t) and they agree naturally before
i.e. F((l,t))(s) = l(ts)
I was wondering if anyone could point me roughly the right way or just chip in with their own thoughts