In an old research paper**, I saw a theorem relating to a correspondence that has an "open graph". I looked for this term in Google, and all I could find was the "open graph" technology of Facebook, which is totally unrelated. So what does it mean that a correspondence has an open graph?
** Equilibrium in abstract economies without ordered preferences, by Shafer and Sonnenschein.
I haven't found a free version available online, but, the paper is summarized in Wikipedia.
EDIT: I should have googled for Closed graph - it is a much more common term.
A correspondence is simply a set-valued map $\phi: X\to 2^Y$. The graph of $\phi$ is then the set $$\Gamma(\phi)=\{(x,y)\in X\times Y\mid y\in\phi(x)\}.$$ If $X$ and $Y$ come endowed with topologies, we can endow $X\times Y$ with the product topology. If the graph of $\phi$ is an open set in the product topology, we say that $\phi$ has an open graph.