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
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.): Part $\text {II}$: Counterexamples: $63$. Countable Complement Extension Topology