Upper bounds of topologies

The topology of a space $(X,\tau)$ homeomorphic to a non-$\sigma$-compact separable Borel set is equal to the upper bound of two topologies of the Hilbert cube. In particular, $(X,\tau)$ condenses to a compact space. The topology of a complete zero-dimensional metric space is the upper bound of two compact topologies. In particular, it dominates a compact Hausdorff topology.