Consider the equivalence relation $‘∼’ $on R × [0, 1] defined by $(x, t) ∼ (x + 1, t), x ∈ R$ and$ t ∈ [0, 1].$ Let $X =(R × [0, 1])/ ∼$ be the quotient space.
Prove that X is Hausdorff and compact.
i was thinking that ,If the quotient map is open, then $X/ \sim$ is a Hausdorff space if and only if $\sim$ is a closed subset of the product space $[0,1]\times X$.
as im very weak in topology and im newly learning topology
pliz help me