Filling boxes densely and disjointly
We effectively construct in the Hilbert cube two sets with the following properties: (a) , (b) is discrete-dense, i.e. dense in , where denotes the unit interval equipped with the discrete topology, (c) , are open in . In fact, , , where , . , are basic open sets and , , (d) , is point symmetric about . Instead of we could have taken any -space or a digital interval, where the resolution (number of points) increases with .