A nowhere convergent series of functions converging somewhere after every non-trivial change of signs
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چکیده
We construct a sequence of continuous functions (hn) on any given uncountable Polish space, such that ∑ hn is divergent everywhere, but for any sign sequence (εn) ∈ {−1,+1} N which contains infinitely many −1 and +1 the series ∑ εnhn is convergent at at least one point. We can even have hn → 0, and if we take our given Polish space to be any uncountable closed subset of R, we can require that every hn be a polynomial. This strengthens a construction of Tamás Keleti and Tamás Mátrai.
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تاریخ انتشار 2008