I am trying to understand the chapter about sheaves in the book by Warner "Foundations of Differentiable Manifolds and Lie Groups". A sheaf $J$ of $K$-modules over $M$ is defined as a topological space $J$ together with a map (called projection) $\pi: J \rightarrow M$ such that
(i) $\pi$ is a local homeomorphism
(ii) $\pi^{-1}(m)$ is a $K$-module for each $m \in M$
(iii) module operations are continuous.
I am puzzled by the first two conditions. My understanding was that homeomorphisms should preserve the dimension. How can its inverse be not a point but say a vector space which is a certain $K$-module?