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$\begingroup$

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

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

Thanks.

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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](http://en.wikipedia.org/wiki/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 $Y$.2012-04-28
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    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](http://books.google.sk/books?hl=sk&id=-o8xJQ7Ag2cC&pg=PA65).2012-04-28
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    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 http://mathdl.maa.org/mathDL/19/?pa=reviews&sa=viewBook&bookId=694212012-09-17

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The question is solved as in the comments.