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Not all dyadic spaces are supercompact. (English) Zbl 0716.54017
Summary: 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 subbase $${\mathcal S}$$ such that every open cover of X consisting of members of $${\mathcal S}$$ 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 [Topology Appl. 13, 21-32 (1982; Zbl 0502.54026)].

##### MSC:
 54D30 Compactness 54G20 Counterexamples in general topology 54B15 Quotient spaces, decompositions in general topology
##### Keywords:
supercompact space; continuous image; dyadic space
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