Moderate# Continuity in the Co-Finite Topology On Natural Numbers

TOPO-BEY15E

Consider $\mathbb{N}$ with co-finite topology.

This means that the open sets are the empty set $\emptyset$ and all $A\subset \mathbb{N}$ such that $A^c:= \mathbb{N}\setminus A$ is a finite set. Let $a$ be the sequence $(a_n)_{n\geq 1}$ defined by $a_n:=n$.

Choose the **INCORRECT** statements from the list.