Even though this sounds plausible, it's actually false. The counterxample is the first uncountable ordinal ω₁ [1], viewed as a well-ordered set (and thus a fortiori totally ordered). For every a,b in ω₁, the closed…
Even though this sounds plausible, it's actually false. The counterxample is the first uncountable ordinal ω₁ [1], viewed as a well-ordered set (and thus a fortiori totally ordered). For every a,b in ω₁, the closed…