Consider the co-presheaf $\mathcal{F}$ of continous real-valued functions with compact support on a topological space $X$. Consider a point $x\in X$.

1. When $\mathcal{F}$ is considered a co-presheaf with values in the category of sets, what is the co-stalk $\mathcal{F}_x$?

2. For X paracompact a partition of unit exists. Hence $\mathcal{F}$ is even a cosheaf when considered with values in the category of real vector spaces. What is the co-stalk $\mathcal{F}_x?$

Consider the co-presheaf $\mathcal{F}$ of continous real-valued functions with relatively-compact support on a topological space $X$. Consider a point $x\in X$.

1. When $\mathcal{F}$ is considered a co-presheaf with values in the category of sets, what is the co-stalk $\mathcal{F}_x$?

2. For X paracompact a partition of unit exists. Hence $\mathcal{F}$ is even a cosheaf when considered with values in the category of real vector spaces. What is the co-stalk $\mathcal{F}_x?$