scholarly journals Pontryagin duality in the class of precompact Abelian groups and the Baire property

2012 ◽  
Vol 216 (12) ◽  
pp. 2636-2647 ◽  
Author(s):  
M. Bruguera ◽  
M. Tkachenko
Keyword(s):  
Abelian Groups ◽  
Baire Property ◽  
Pontryagin Duality

Pego everywhere

2016 ◽  
Vol 15 (04) ◽  
pp. 1650074 ◽  
Author(s):  
Przemysław Górka ◽  
Tomasz Kostrzewa
Keyword(s):  
Fourier Transform ◽  
Abelian Groups ◽  
General Version ◽  
Pontryagin Duality ◽  
Locally Compact ◽  
Locally Compact Abelian Groups ◽  
Compact Abelian Groups ◽  
The Fourier Transform ◽  
Compact Subsets

In this note we show the general version of Pego’s theorem on locally compact abelian groups. The proof relies on the Pontryagin duality as well as on the Arzela–Ascoli theorem. As a byproduct, we get the characterization of relatively compact subsets of [Formula: see text] in terms of the Fourier transform.

scholarly journals The Pontryagin duality of sequential limits of topological Abelian groups

2005 ◽  
Vol 202 (1-3) ◽  
pp. 11-21 ◽  
Author(s):  
S. Ardanza-Trevijano ◽  
M.J. Chasco
Keyword(s):  
Abelian Groups ◽  
Pontryagin Duality

scholarly journals Nilpotent groups are not dualizable

2002 ◽  
Vol 72 (2) ◽  
pp. 173-180 ◽  
Author(s):  
R. Quackenbush ◽  
C. S. Szabó
Keyword(s):  
Finite Group ◽  
Abelian Group ◽  
Abelian Groups ◽  
Finite Abelian Group ◽  
Nilpotent Groups ◽  
Nilpotent Subgroup ◽  
Pontryagin Duality ◽  
Sylow Subgroups ◽  
Companion Article

AbstractIt is shown that no finite group containing a non-abelian nilpotent subgroup is dualizable. This is in contrast to the known result that every finite abelian group is dualizable (as part of the Pontryagin duality for all abelian groups) and to the result of the authors in a companion article that every finite group with cyclic Sylow subgroups is dualizable.

Pontryagin duality for topological Abelian groups

2001 ◽  
Vol 238 (3) ◽  
pp. 493-503 ◽  
Author(s):  
Salvador Hern�ndez
Keyword(s):  
Abelian Groups ◽  
Pontryagin Duality

scholarly journals An extension of Pontryagin duality

1978 ◽  
Vol 19 (3) ◽  
pp. 445-456 ◽  
Author(s):  
B.J. Day
Keyword(s):  
Closed Subgroup ◽  
Full Subcategory ◽  
Abelian Groups ◽  
Pontryagin Duality ◽  
Locally Compact ◽  
Limit Space ◽  
Closed Category ◽  
Continuous Convergence ◽  
Symmetric Monoidal Closed Category ◽  
Monoidal Closed Category

Let V denote the symmetric monoidal closed category of limit-space abelian groups and let L denote the full subcategory of locally compact Hausdorff abelian groups. Results of Samuel Kaplan on extension of characters to products of L–groups are used to show that each closed subgroup of a product of L-groups is a limit of L–groups. From this we deduce that the limit closure of L in V is reflective in V and has every group Pontryagin reflexive with respect to the structure of continuous convergence on the character groups. The basic duality L ≃ Lop is then extended.

WEAK REFLECTION IN CONCRETE CATEGORIES

2001 ◽  
Vol 37 (1-2) ◽  
pp. 185-193
Author(s):  
G. Hegedűs
Keyword(s):  
Vector Space ◽  
Abelian Groups ◽  
Vector Spaces ◽  
Space Structures ◽  
Pontryagin Duality ◽  
Weak Reflection

In this art cle I give the de .n t on of the strong and weak re .ex v ty and the com- pat bility relation of objects in a categorical language.These concepts will generalize the corresponding concepts n the theory of topolog cal vector spaces. The main theorem makes clear the connection between these mportant concepts and we can show a lot of objects in our category,which are not strongly re .exive,but compatible with strongly re .ex ve objects.We also consider a lot of interesting examples and try to throw new light upon the ex stence of such Abelian groups which satisfy Pontryagin duality but do not respect compactness.We w ll prove also that the weak topolog cal vector space- structures are not re .ex ve in general.

scholarly journals On Pontryagin duality

1979 ◽  
Vol 20 (1) ◽  
pp. 15-24 ◽  
Author(s):  
B. J. Day
Keyword(s):  
Lie Groups ◽  
Abelian Groups ◽  
Pontryagin Duality ◽  
Locally Compact ◽  
The Relationship

The main aim of this article is to discuss the relationship between Pontryagin duality and pro-objects. The basic idea arises from K. H. Hofmann's articles [7] and [8] where it is shown that the elementary abelian (Lie) groups are “dense” in the category of locally compact hausdorff abelian groups.

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