I'm assigned a homework problem as follows:
Let $X$ be the Möbius strip, obtained as a quotient space of $[0,1] \times [0,1]$ (with subspace topology of $\mathbb{R}^2$) by identifying the pairs of points $(0,1) \sim (1, 1-y)$ for $0\leq y \leq 1$. Let $p: [0,1] \times [0,1] \rightarrow X$ be the associated quotient map. Let $A=\{(x,y) \in [0,1]\times[0,1] \mid y=0\text{ or }y=1 \}$. Show that $p(A)$ is homeomorphic to a circle.
I'm not sure where to start and can't seem to find an answer for the problem on this community. Please help. Thank you!