A note on stably closed maps of locales (Q5931440)

Let \(X,Y,Z\) be locales. The principal result of this paper asserts that a map \(f:X\rightarrow Y\) is a closed map and the left adjoint \(f_{!}:\text{QTR}{\mathfrak C}_{Y}\rightarrow \text{QTR}{\mathfrak C}_{X}\) to taking inverse images of closed sublocales preserves filtered infima whenever \(id\times f:Z\times Y\rightarrow Z\times X\) is closed for all \(Z\).