Disjoint Union
المؤلف:
Armstrong, M. A
المصدر:
Basic Topology, rev. ed. New York: Springer-Verlag, 1997.
الجزء والصفحة:
...
11-1-2022
959
Disjoint Union
The disjoint union of two sets 
and 
is a binary operator that combines all distinct elements of a pair of given sets, while retaining the original set membership as a distinguishing characteristic of the union set. The disjoint union is denoted
![A union ^*B=(A×<span style=]() {0}) union (B×{1})=A^* union B^*, " src="https://mathworld.wolfram.com/images/equations/DisjointUnion/NumberedEquation1.gif" style="height:15px; width:238px" /> |
(1)
|
where 
is a Cartesian product. For example, the disjoint union of sets ![A=<span style=]()
{1,2,3,4,5}" src="https://mathworld.wolfram.com/images/equations/DisjointUnion/Inline4.gif" style="height:15px; width:103px" /> and ![B=<span style=]()
{1,2,3,4}" src="https://mathworld.wolfram.com/images/equations/DisjointUnion/Inline5.gif" style="height:15px; width:88px" /> can be computed by finding
 |
 |
![<span style=]() {(1,0),(2,0),(3,0),(4,0),(5,0)}" src="https://mathworld.wolfram.com/images/equations/DisjointUnion/Inline8.gif" style="height:15px; width:192px" /> |
(2)
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 |
![<span style=]() {(1,1),(2,1),(3,1),(4,1)}," src="https://mathworld.wolfram.com/images/equations/DisjointUnion/Inline11.gif" style="height:15px; width:158px" /> |
(3)
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so
 |
 |
 |
(4)
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 |
 |
![<span style=]() {(1,0),(2,0),(3,0),(4,0),(5,0),(1,1),(2,1),(3,1),(4,1)}." src="https://mathworld.wolfram.com/images/equations/DisjointUnion/Inline17.gif" style="height:15px; width:348px" /> |
(5)
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REFERENCES:
Armstrong, M. A. Basic Topology, rev. ed. New York: Springer-Verlag, 1997.
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