Suppose $f: \mathcal{X}\rightarrow Y$ is a morphism from an algebraic stack $\mathcal{X}$ to a scheme $Y$. It can induce a unique topological morphism $|f|:\mathcal{|X|}\rightarrow Y$.
Suppose $y\in Y$ is a point of $Y$, my question is if $|f|^{-1}(y)\subseteq |\mathcal{X}|$ with the induced topology, homeomoephic to $|\mathcal{X}\times_Y k(y)|$?
Any comment would be appreciated.
I give a look-like proof for $Y=Spec \mathbb{Z}$. For arbitary scheme $Y$ the proof should be the same. I have to say show these stuff looks very sloppy.
