Definiton: A sheaf of abelian groups on $X$ is a topological space $F$ together with a mapping $f:F\to X$, such that
1.$f$ is local homemorphism
2.for each $p\in X$ the set $f^{-1}(p)$,called the stalk at $p$ is abelian group
3.the group operations are continuous in the topology of $F$. ie. define $F \times_{f} F$={$(a,b)\in F\times F:f(a)=f(b)$}, then the mapping $F \times_{f} F\to F$ by $(a,b)\mapsto a-b$ is continuous.
What I really not understand is that the group operation is continuous. I want to show that $+:f^{-1}(p)\times f^{-1}(p)\to f^{-1}(p)$ with $(a,b)\mapsto a+b$ is continuous under subspace topology, which equivalent to show that $f^{-1}(p) \to f^{-1}(p)$ by $a\mapsto -a$ is homeomorphsim , can someone help me this question, thanks