Correction to duality and harmonic analysis on central topological groups
نویسندگان
چکیده
منابع مشابه
On Duality of Topological Abelian Groups
Let G denote the full subcategory of topological abelian groups consisting of the groups that can be embedded algebraically and topologically into a product of locally compact abelian groups. We show that there is a full coreflective subcategory S of G that contains all locally compact groups and is *-autonomous. This means that for all G,H in S there is an “internal hom” G −◦H whose underlying...
متن کاملNormed versus topological groups: Dichotomy and duality
The key vehicle of the recent development of a topological theory of regular variation based on topological dynamics [BOst-TRI], and embracing its classical univariate counterpart (cf. [BGT]) as well as fragmentary multivariate (mostly Euclidean) theories (eg [MeSh], [Res], [Ya]), are groups with a right-invariant metric carrying flows. Following the vector paradigm, they are best seen as norme...
متن کاملElements of Harmonic Analysis, 3 Locally Compact Abelian Topological Groups
Let A be an abelian group. Thus A is a set equipped with a binary operation + which is commutative and associative, there is an identity element 0 ∈ A such that 0 + a = a for all a ∈ A, and each a ∈ A has an inverse −a characterized by a + (−a) = 0. As basic examples, the integers, real numbers, and complex numbers are abelian groups under addition, and for each positive integer n we have the i...
متن کاملNon-productive Duality Properties of Topological Groups
We address two properties for Abelian topological groups: “every closed subgroup is dually closed” and “every closed subgroup is dually embedded.” We exhibit a pair of topological groups such that each has both of the properties and the product has neither, which refutes a remark of N. Noble. These examples are the additive group of integers topologized with respect to a convergent sequence as ...
متن کاملContinuous Convergence and Duality of Limits of Topological Abelian Groups
We find conditions under which direct and inverse limits of arbitrary indexed systems of topological Abelian groups are related via the duality defined by the continuous convergence structure. This generalizes known results by Kaplan about duality of direct and inverse sequences of locally compact Abelian groups.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Indagationes Mathematicae (Proceedings)
سال: 1973
ISSN: 1385-7258
DOI: 10.1016/1385-7258(73)90036-x