Suppose we consider the unit square $[0,1]^2$ in $\mathbb{R}^2$ with the relative topology. Define an equivalence relation $R = \{((x,y),(x',y') | x = x' = 0,$ or $(x,y) = (x',y')\}$.
Intuitively, the left side of the unit square collapses to a single point. Is there a better way to describe the quotient space?
Edit: I think this might just be a triangle, since we can continuously deform the square in such a way.
Indeed the left edge is identified to a point. The result could be described as a triangle, or a square again, or a disk (these are topologically the same).