The following question is from my topology assignment and I was unable to solve it.
Consider the equivalence relation $\sim$ on $\mathbb{R} \times [0,1] $ defined by $(x,t) \sim (x+1, t)$, $x\in \mathbb{R}$ and $t\in [0,1]$. Let $ X= (\mathbb{R} \times [0,1]) / \sim $ be the quotient space. Prove that $X$ is Hausdorff and compact.
I have studied Quotient Space from Wayne Patty but I am not good at solving problems of quotient topology. It is my weak point despite reading the theory a lot of times.
So, it is my very humble request can you please give some hints for this question. I shall be really thankful.