\(L\)-topological meet theorems (Q2386244)

Let \(\{C_ x:\;x\in X\}\) be a family of subsets of some set \(Y\). A topological condition was given in [\textit{J. Kindler}, Proc. Am. Math. Soc. 117, 1003--1011 (1993; Zbl 0774.54016)] that is both necessary and sufficient for \(\bigcap\{C_ x: x\in X\}\) to be nonvoid. In this paper the authors extend this result to the lattice-valued setting by a proper choice of compactness and connectedness for lattice valued topological spaces.