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I'm reading "General Topology" by Muller and he uses $$A \amalg B = \{(1, a) | a ∈ A\} ∪ \{(2, b) | b ∈ B\}.$$ Does this operation have a name or a different symbol? I've never seen it before.

djeastm
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  • Looks like a "disjoint union" or "co-product" Is the symbol exactly what you used here or rather $\coprod$ a flipped product sign? – quid Aug 31 '17 at 21:53
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    Looking more closely, it is indeed a flipped product sign ∐. I appreciate the clarification. – djeastm Aug 31 '17 at 22:03
  • Out of interest, does Muller use $\amalg$ or $\sqcup$? $\amalg$ is usually used for the disjoint union of a family of sets, not just two sets (cf. $\sum$ v. $+$). – Rob Arthan Aug 31 '17 at 22:10
  • $\amalg$. He starts with "If A and B are sets..." – djeastm Sep 01 '17 at 11:46

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The symbol is actually $\coprod$, and this operation is called "disjoint union". The idea is you are taking the union of $A$ and $B$, except you are forcing them to be disjoint sets first. The symbol is kind of a pun. On the one hand, it is a variant of the union symbol $\cup$. On the other hand, it is an upside down version of the product symbol $\prod$, and $\coprod$ is also called the "coproduct" since it is dual in a certain sense to the Cartesian product of sets.

Eric Wofsey
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