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Small Combinatorial Cardinal Characteristics And Theorems Of Egorov And Blumberg, Krzysztof Ciesielski
Small Combinatorial Cardinal Characteristics And Theorems Of Egorov And Blumberg, Krzysztof Ciesielski
Faculty & Staff Scholarship
We will show that the following set theoretical assumption
- \continuum=\omega2, the dominating number d equals to \omega1, and there exists an \omega1-generated Ramsey ultrafilter on \omega
(which is consistent with ZFC) implies that for an arbitrary sequence fn:R-->R of uniformly bounded functions there is a subset P of R of cardinality continuum and an infinite subset W of \omega such that {fn|P: n in W} is a monotone uniformly convergent sequence of uniformly continuous functions. Moreover, if functions fn are measurable or have the …