Cardinal Invariants for the $G_{\delta }$ topology

We prove upper bounds for the spread, the Lindel"of number and the weak Lindel"of number of the $G_{\delta }$-topology on a topological space and apply a few of our bounds to give a short proof to a recent result of Juh'asz and van Mill regarding the cardinality of a $\sigma$-countably tight homogeneous compactum.