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$$X\cup_f Y = (X\amalg Y)/\{f(A)\sim A\}$$

This is the definition of adjunction space in Wikipedia. I wasn't able to understand some signs: $/$ and $\amalg$. What do they mean?


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$\coprod$ means the disjoint union with the corresponding topology (a set is open if and only if it is the union of an open set in $X$ and an open set in $Y$). $/$ means that you are taking the quotient space on the disjoint union of $X$ and $Y$ with respect to the equivalence relation that identifies $x\in A=\mathrm{dom}(f)$ with its image $f(x)$ in $Y$. – Arturo Magidin Apr 28 '12 at 4:47
Some explanation is given in the Wikipedia article, too: "One forms the adjunction space $X \cup_f Y$ by taking the disjoint union of $X$ and $Y$ and identifying $x$ with $f(x)$ for all $x$ in $A$." Wikipedia article mentions Willard's book as a reference, so it might be useful to look there: p.65. – Martin Sleziak Apr 28 '12 at 4:58
There is much more on adjunction spaces, including their homotopy type, in my book "Topology and Groupoids" available from amazon sites. See an MAA review here… – Ronnie Brown Sep 17 '12 at 16:53
up vote 1 down vote accepted

The question is solved as in the comments.

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