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Product (mathematics)
About: Product (mathematics) is a research topic. Over the lifetime, 44382 publications have been published within this topic receiving 377809 citations.
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TL;DR: In this paper, the exponential law for function spaces with the compact-open topology is discussed, and the main result is that the spaces X and (X) are homeomorphic for all X, Y, Z (in this paper ZxY will denote the product ZxsY defined in (4), and ZxX will represent the usual, cartesian, product).
Abstract: Introduction IN a previous paper (4) I defined ten product topologies o n l x T . In this paper five of these products are applied to problems on function spaces. All spaces will be Hausdorff spaces. The exponential law for function spaces with the compact-open topology is discussed in § 1. The main result (Theorem 1.6) is that the spaces X and (X) are homeomorphic for all X, Y, Z (in this paper ZxY will denote the product ZxsY defined in (4), and ZxY will denote the usual, cartesian, product). Hence the exponential law holds for ZxY if Z x 7 = ZxF , and this contains and explains many known results. We deduce also some new results. For example we prove that the answer is 'no' to Dr. S. Wylie's question: are the spaces (X) and (X) naturally homeomorphic? In § 2 we discuss the law (XxY) = XxY. This fails in general for products other than the cartesian. .§ 3 is the most important section. It advertises the category of Hausdorff spaces and functions continuous on compact subspaces (here called k-continuous functions). In § 4 the exponential law of § 3 is generalized to the category of .if-ads. I am indebted to a referee, whose comments stimulated a complete revision and extension of the original draft, and to Dr. M. G. Barratt for the inspiration of his conversation and example. I am also indebted to Dr. W. F. Newns and Professor A. Dold for helpful conversations.
85 citations
Patent•
27 Aug 2009
TL;DR: In this paper, a computerized method for storing purchase information for a product in a price database to generate a purchase history was proposed, where the set of sales information includes a product identifier for the product and a price.
Abstract: A computerized method for storing purchase information for a product in a price database to generate a purchase history includes receiving in a price database a set of sales information for a product, wherein the set of sales information includes a product identifier for a product and a price for the product; and storing in the price database a price entry, which include the set of sales information, wherein the price entry is editable to generate a purchase history.
85 citations
TL;DR: In this paper, it was shown that the Jacobian of the Nth Fermat curve is isogenous over C. The purpose of this paper is to determine when two factors in this product are isogenous over C, and whether they are absolutely simple.
Abstract: Let denote the Nth Fermat curve. The period lattice of F(N) is contained with finite index in the product of certain lattices Lr,s (see [6]), and to this inclusion of lattices there corresponds an isogeny of the Jacobian of F(N) onto a product of abelian varieties. The purpose of this paper is to determine when two factors in this product are isogenous over C, and whether they are absolutely simple.
85 citations
TL;DR: In this article, the authors studied the restrictions of simple modules of Ariki-Koike algebras H m(v) with set of parametersv=(ζ; ζv0, εv1, δv2,εvl−1), where ε is the annth root of unity.
85 citations
Journal Article•
85 citations