Not all dyadic spaces are supercompact
Murray G. Bell · Czech digital mathematics library · 1990
A space is called dyadic if it is a Hausdorff continuous image of some power of the discrete space 2. A space X is called supercompact if it possesses an open sub base S such that every open cover of X consisting of members of S has an at most 2 subcover.We show that there is an example of a dyadic space which is not supercompact thus answering a question of E. van Douwen and J. van Mill.