On a typical series with alternating signs (Q1852314)

This paper is a continuation of a previous paper by the author [Real. Anal. Exch. 25, 599-616 (2000; Zbl 1011.40002)]. Here he deals with series of the form \[ \sum^\infty_{n=1}(-1)^{a_n} b_n,\tag{1} \] where \((a_n)^\infty_1\in \{0,1\}^{\mathbb{N}}, b_n\) \((n= 1,2,\dots)\) are real numbers. He shows that if \(\sum^\infty_{n=1} b_n= +\infty\), then each of the sets \(C= \{(a_n)^\infty_1\in \{0,1\}^{\mathbb{N}}\): (1) converges\}, \(B= \{(a_n)^\infty_1\in \{0,1\}^{\mathbb{N}}\): (1) is bounded\} is a set of the first category of the (complete) metric spaces \((\{0,1\}^{\mathbb{N}},d_{\text{F}})\) and \((\{0,1\}^{\mathbb{N}}, d_{\text{B}})\), where \(d_{\text{F}}\) and \(d_{\text{B}}\) are the Fréchet and Baire metrics, respectively. These results are completed by a porosity investigation of sets \(B\), \(C\) for a class of series \(\sum^\infty_{n=1} b_n\).