Definition:Countable Complement Extension Topology

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Theorem

Let $\R$ denote the real number line.

Let $\tau_d$ be the Euclidean topology on $\R$.

Let $\tau_c$ be the countable complement topology $\R$.


Let $\tau$ be the smallest topology generated by $\tau_c \cup \tau_d$.


$\tau$ is known as the countable complement extension topology on $\R$.


Also see

  • Results about the countable complement extension topology can be found here.


Sources