Usual set theoretic notation is employed, though note that T is a multiset.
2.
This problem is among twenty of the most important problems of set theoretic topology.
3.
The Zariski topology in the set theoretic sense is then replaced by a Grothendieck topology.
4.
In this context, many set theoretic ideas about domains must be abandoned or at least formulated more abstractly.
5.
What you said about understanding the set theoretic definition of a topology struck a chord with me, though.
6.
The two preceding examples are power sets, which are Boolean algebras under the usual set theoretic operations of union, intersection, and complement.
7.
As shown by Ilijas Farah and N . Christopher Phillips and Nik Weaver, the existence of outer automorphisms of the Calkin algebra depends on set theoretic assumptions beyond ZFC.
8.
X . Introduced November 1969, Dana Scott's untyped set theoretic model constructed a proper topology for any ?-calculus model whose function space is limited to continuous functions.
9.
Note that there are other notions of compactness in mathematics; also, the term " set theoretic meaning does not coincide with the order-theoretic notion of a " finite element ".
10.
This definition of intersection multiplicity, which is essentially due to Jean-Pierre Serre in his book " Local algebra ", works only for the set theoretic components ( also called " isolated components " ) of the intersection, not for the embedded components.
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