The general position number under vertex and edge removal

Let $\mathrm{g}\mathrm{p}(G)$ be the general position number of a graph $G$. It is proved that $\mathrm{g}\mathrm{p}(G-x)\le 2\mathrm{g}\mathrm{p}(G)$ holds for any vertex $x$ of a connected graph $G$ and that if $x$ lies in some $\mathrm{g}\mathrm{p}$-set of $G$, then $\mathrm{g}\mathrm{p}(G)-1\le \mathrm{g}\mathrm{p}(G-x)$. Constructions are given which show that $\mathrm{g}\mathrm{p}(G-x)$ can be much larger than $\mathrm{g}\mathrm{p}(G)$ also when $G-x$ is connected. For diameter $2$ graphs it is proved that $\mathrm{g}\mathrm{p}(G-x)\le \mathrm{g}\mathrm{p}(G)$, and that $\mathrm{g}\mathrm{p}(G-x)\ge \mathrm{g}\mathrm{p}(G)-1$ when the diameter of $G-x$ remains $2$. It is demonstrated that $\mathrm{g}\mathrm{p}(G)\mathrm{/}2\le \mathrm{g}\mathrm{p}(G-e)\le 2\mathrm{g}\mathrm{p}(G)$ holds for any edge $e$ of a graph $G$. For diameter $2$ graphs these results can be improved to $\mathrm{g}\mathrm{p}(G)-1\le \mathrm{g}\mathrm{p}(G-e)\le \mathrm{g}\mathrm{p}(G)+1$. All these bounds are proved to be sharp.