Distributive Lattices and Hurewicz families

Abstract

Hurewicz and Rothberger respectively introduced prototypes of the selection properties Sfin(A, B) and S1(A, B). In the series of papers titled "Combinatorics of open covers" (see the bibliography) we learned that for various topologically significant families A and B these selection properties are intimately related to game theory and Ramsey theory. The similarity in techniques used there to explore these relationships suggests that there should be a general, unified way to obtain these results. In this paper we pursue one possibility by considering the selection principle Sfin(A,B) for distributive lattices. The selection principle S1(A, B) for distributive lattices will be treated in [3]. We use two examples throughout to illustrate the generality of the methods developed here.

Locations

• Mathematica Moravica - View - PDF