when I am learning topology, specifically identification space, I have a confusion about this question.
Consider the following Mobius strip: $M = [0,1]*[0,1]/(0,y)$ ~ $(1, 1 - y)$ and the closed unit circle $D = ${$(\rho, \theta)| \rho\leq1$}.
And then we have a map: $f(1, \theta) = (\theta/\pi, 1)$ if $0\leq\theta\leq\pi$ or $= (\theta/\pi -1, 0)$if $\pi\leq\theta\leq2\pi$ . I think such a map maps the boundary of the unit disc, a circle, to the boundary of the Mobius strip, right?
The question asks me to explain what is the following identification map:
$D \cup_fM$. I am not quite certain what does this question mean, what does the identification space mean?
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