Mostre que cada parcela de $\{x_{\xi} : \xi < \mathfrak{c}\} \cap F_{\xi} = \big(\{x_{\xi} : \xi < \mathfrak{c}\} \cap F_{\xi} \cap \bigcup_{\zeta < \xi} F_{\zeta} \big) \cup \big(\{x_{\xi} : \xi < \mathfrak{c}\} \cap F_{\xi} \cap \mathbb R \setminus \bigcup_{\zeta < \xi} F_{\zeta}\big)$ é enumerável.