منابع مشابه
Stone duality, topological algebra, and recognition
Our main result is that any topological algebra based on a Boolean space is the extended Stone dual space of a certain associated Boolean algebra with additional operations. A particular case of this result is that the profinite completion of any abstract algebra is the extended Stone dual space of the Boolean algebra of recognisable subsets of the abstract algebra endowed with certain residuat...
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Then H need not be divisible, i.e., we need not have pH D H . We only know H is contained in pG. Moreover, for x in H , there need not exist an infinite sequence y1;y2;y3:::: such that py2 D y1, py3 D y2; ::. We only know that there exist arbitrarily long finite such sequences. There does exist a unique maximal divisible subgroup D of M , and D is a subgroup of H . Moreover, M DD ̊N where N is a...
متن کاملDuality in Algebra and Topology
In this paper we take some classical ideas from commutative algebra, mostly ideas involving duality, and apply them in algebraic topology. To accomplish this we interpret properties of ordinary commutative rings in such a way that they can be extended to the more general rings that come up in homotopy theory. Amongst the rings we work with are the differential graded ring of cochains on a space...
متن کاملCurves and Topological Algebra
Let ε 3 ∞ be arbitrary. Recently, there has been much interest in the description of covariant, pseudo-characteristic, Littlewood arrows. We show that every maximal domain is commutative. This leaves open the question of admissibility. In contrast, recent developments in applied arithmetic [3] have raised the question of whether GP ( Q̂, . . . , 1 N ) = ∫∫∫ Γ ( UPλ, . . . , 1 2 ) dW ∨ · · ·+ β (...
متن کاملTopological Field Theories and Duality
Topologically non trivial effects appearing in the discussion of duality transformations in higher genus manifolds are discussed in a simple example , and their relation with the properties of Topological Field Theories is established.
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1978
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700008613