Note that in object-oriented programming languages, such as Java, a disjoint union can be expressed by designing class hierarchies.
32.
A simpler cobordism between " M " and " N " is given by the disjoint union of three disks.
33.
A circular order on the disjoint union } is defined by, where the induced ordering on is the opposite of its original ordering.
34.
Likewise, a horizontal bundle is the disjoint union of the horizontal subspaces H " e " " E ".
35.
Let " Y " be the disjoint union of the " X i ", so that there is a natural mapping
36.
The Hilbert scheme breaks up as a disjoint union of pieces corresponding to the Hilbert polynomial of the subschemes of projective space with Hilbert polynomial.
37.
Additionally, a disjoint union of two graphs that have covers will also have a cover, formed as the disjoint union of the covering graphs.
38.
Additionally, a disjoint union of two graphs that have covers will also have a cover, formed as the disjoint union of the covering graphs.
39.
As such, the disjoint union is defined up to an isomorphism, and the above definition is just one realization of the coproduct, among others.
40.
This categorical aspect of the disjoint union explains why \ coprod is frequently used, instead of \ bigsqcup, to denote " coproduct ".
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