$\pi_0(X) \cong [*,X]$

Question

Let $\pi_0(X)$ denote the set of path components of a space X.

I want to show that $\pi_0(X)$ is the set of homotopy classes of maps from the one point space ∗ to X, by constructing a bijection

but I am unsure of where to start. Any help or hints would be appreciated.

score 3 · Accepted Answer · answered Nov 04 '17 at 16:59

3

Hint: Given a homotopy $H\colon I\times *\to X$, $H(*,t)\in X$, can you find a path in $X$?

answered Nov 04 '17 at 16:59

ziggurism

1 Answers1