path

Definition

Let $X$ be a topological space, and $x,y\in X$. A path from $x$ to $y$ is a continuous function

$\gamma :I⟶X$

such that $\gamma (0)=x$ and $\gamma (1)=y$ .

(basically the same thing as a curve, just for simplicity we have it always on the interval $[0,1]$.)