Abstract
The operation of symmetric difference, defined by
is commutative, associative, and satisfies the distributive law A ∩ (B △ C) = (A ∩ B) △ (A ∩ C). Evidently, A △ B ⊂ A ∪ B and \(A\,\Delta \,A = \emptyset\). It is easy to verify that any class of sets that is closed under △ and ∩ is a commutative ring (in the algebraic sense) when these operations are taken to define addition and multiplication, respectively. Such a class is also closed under the operations of union and difference. It is therefore a ring of subsets of its union, as this term was defined in Chapter 3.
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© 1971 Springer-Verlag New York
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Oxtoby, J.C. (1971). The Property of Baire. In: Measure and Category. Graduate Texts in Mathematics, vol 2. Springer, New York, NY. https://doi.org/10.1007/978-1-4615-9964-7_4
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DOI: https://doi.org/10.1007/978-1-4615-9964-7_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-05349-3
Online ISBN: 978-1-4615-9964-7
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