Locally compact products and coproducts in categories of topological groups
نویسندگان
چکیده
منابع مشابه
Bracket Products on Locally Compact Abelian Groups
We define a new function-valued inner product on L2(G), called ?-bracket product, where G is a locally compact abelian group and ? is a topological isomorphism on G. We investigate the notion of ?-orthogonality, Bessel's Inequality and ?-orthonormal bases with respect to this inner product on L2(G).
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A product and coproduct in categories are introduced. The concepts included correspond to that presented in 7]. and 6] provide the notation and terminology for this paper.
متن کاملProducts and Coproducts in Categories
The scheme FuncIdx correctness deals with a set A , a non empty set B, and a unary functor F yielding an element of B, and states that: (i) There exists a function F from A into B such that for every x such that x ∈ A holds Fx = F (x), and (ii) for all functions F1, F2 from A into B such that for every x such that x ∈ A holds (F1)x = F (x) and for every x such that x∈A holds (F2)x = F (x) holds...
متن کاملbracket products on locally compact abelian groups
we define a new function-valued inner product on l2(g), called ?-bracket product, where g is a locally compact abelian group and ? is a topological isomorphism on g. we investigate the notion of ?-orthogonality, bessel's inequality and ?-orthonormal bases with respect to this inner product on l2(g).
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Let $pounds$ be the category of locally compact abelian groups and $A,Cin pounds$. In this paper, we define component extensions of $A$ by $C$ and show that the set of all component extensions of $A$ by $C$ forms a subgroup of $Ext(C,A)$ whenever $A$ is a connected group. We establish conditions under which the component extensions split and determine LCA groups which are component projective. ...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1977
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700010674