Take the 2-minute tour ×

Let X be a (finite dimensional) manifold. Consider smooth mapping space $$PX = C^\infty(I, X)$$ where I = [0,1] is the closed interval. Is this space paracompact? What if we fix a point x in X and consider the pointed path space, is this space paracompact?

share|improve this question

1 Answer 1

up vote 3 down vote accepted

What topology do you want on $C^\infty(I,X)$? One natural topology, the one of uniform convergence of all derivatives, is metrizable, so paracompact.

share|improve this answer

Your Answer


