1.$R$ be equipped with the cofinite topology. Is $R$ connected?
2.$R$ be equipped with the standard topology. Is $R$ connected?
3.$R$ be equipped with the half-open interval topology. Is $R$ connected?
I think that 3 is FALSE. but I don't know that 1,2 are connected
How should i prove that first and second are connected?
Thank you for your answer.