Let $X$ be the topologist's sine curve (i.e. $\left\lbrace (x,y): y=\sin\left(\frac{1}{x}\right),x\in ]0,1]\right\rbrace\cup \lbrace (0,y): y\in [-1,1]\rbrace$) with an arc joining $(0,0)$ and $(1,\sin(1))$, without intersecting the topologist's sine curve.
On the other hand, let's consider the following definition for an aspherical space $X$ : A topological space $X$ is said to be aspherical if given any continuous $f:S^{n}\rightarrow X$, there is an extension $g:D_{n+1}\rightarrow X$ (where $D_{n+1}=\lbrace x\in\mathbb{R}^{n+1}:||x||\leq 1\rbrace$), for any $n\in\mathbb{N}_{0}$.
Can somebody help me/give reference/tell me how I see that $X$ is aspherical but not contractible ?
Thanks a lot!