Let $\mathcal{F}$ be a sheaf of abelian groups on a topological space $X$. For a closed subset $K$ of $X$ define $\Gamma(K,\mathcal{F})$ to be the direct limit of $\mathcal{F}(U)$, where $U$ is an open subset of $X$ containing $K$. Clearly, $\Gamma(K,\mathcal{F})$ is an abelian group and for two closed subsets $K_{1},K_{2}$ of $X$, $K_{1}\subseteq K_{2}$, the canonical restriction map $\rho_{K_{1},K_{2}}:\Gamma(K_{2},\mathcal{F})\mapsto\Gamma(K_{1},\mathcal{F})$ is a group homomorphism.
Now, for two closed sets $T_{1},T_{2}$ of $X$ with $T_{1} \cap T_{2}\neq\phi$ choose $f_{1}\in\Gamma(T_{1},\mathcal{F}),f_{2}\in\Gamma(T_{2},\mathcal{F})$ s.t. $\rho_{T_{1}\cap T_{2},T_{1}}(f_{1})=\rho_{T_{1}\cap T_{2},T_{2}}(f_{2})$. From the gluing axiom of $\mathcal{F}$, can we find $f\in\Gamma(T_{1}\cup T_{2},\mathcal{F})$ s.t. $\rho_{T_{i},T_{1}\cup T_{2}}(f)=f_{i},i=1,2~?$