Well order the real numbers, let [tex] {a_n}_{n \in S_{\Omega} } [/tex] be the the singleton sets of odd numbers in the well order (i.e. skip a number, grab a number, skip a number, grab a number). Since the real numbers are [tex] T_1 [/tex] then singleton sets are closed. [tex] \mathbb{R} [/tex] as a topological space is closed by definition. Let [tex] U := \mathbb{R} \bigcap_{n \in S_{\omega} } {a_n} [/tex] . Then U is closed and hence [tex] \mathbb{R} \backslash U [/tex] is open.(adsbygoogle = window.adsbygoogle || []).push({});

Is my logic correct here? It just seemed strange to me that this set would be open. Does anyone know what this set would look like? Thanks.

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# What would this open set in R look like?

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