#### 22 Citations

Coproduct in the category of groups satisfying Pontryagin duality

- Mathematics
- 1983

Although coproducts exist in the category of topological abelian groups, the coproduct topology is not in general the asterisk topology. However in the subcategory of topological groups satisfying… Expand

Interval of group topologies satisfying Pontryagin duality

- Mathematics
- 1977

Hewitt [2] proved that the only locally compact group topology on the additive group 1R of real numbers strictly finer than the usual topology is the discrete topology. Suppose instead we ask the… Expand

Characterization, structure and analysis on abelian ℒ∞ groups

- Mathematics
- 1985

An abelian topological group is an ℒ∞ group if and only if it is a locally σ-compactk-space and every compact subset in it is contained in a compactly generated locally compact subgroup. Every… Expand

Generalised Kawada–Satake method for Mackey functors in class field theory

- Mathematics
- 2018

We propose and study a generalised Kawada–Satake method for Mackey functors in the class field theory of positive characteristic. The root of this method is in the use of explicit pairings, such as… Expand

On reflexivity and the Ascoli property for free locally convex spaces

- Mathematics
- 2018

Let $L(X)$ be the free locally convex space over a Tychonoff space $X$. If $X$ is Dieudonn\'{e} complete (for example, metrizable), then $L(X)$ is a reflexive group if and only if $X$ is discrete.… Expand

Characteristic Functionals of Probabilistic Measures in DS-Groups and Related Topics

- Mathematics
- 2015

This monograph is devoted to some problems of the theory of probabilistic distributions in topological Abelian groups with sufficiently abundant dual groups.

A survey on reflexivity of abelian topological groups

- Mathematics
- 2012

The Pontryagin duality theorem for locally compact abelian groups (briefly, LCA groups) has been the starting point for many different routes of research in Mathematics. From its appearance there was… Expand

Pontryagin duality for Abelian s- and sb-groups ✩

- Mathematics
- 2011

The main goal of the article is to study the Pontryagin duality for Abelian sand sb-groups. Let G be an infinite Abelian group and X be the dual group of the discrete group Gd. We show that a dense… Expand

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

- Mathematics
- 2011

We present a wide class of reflexive, precompact, non-compact, Abelian topological groups G determined by three requirements. They must have the Baire property, satisfy the open refinement condition,… Expand

Precompact noncompact reflexive Abelian groups

- Mathematics
- 2010

Abstract. We study Pontryagin reflexivity in the class of precompact topological Abelian groups. We find reflexive groups among precompact not pseudocompact and among pseudocompact not compact… Expand

#### References

SHOWING 1-6 OF 6 REFERENCES

$k$-groups and duality

- Mathematics
- 1970

Recall that a function is Ac-continuous if its restriction to each compact subset of its domain is continuous. We call a topological group G a Ac-group if each ¿-continuous homomorphism on G is… Expand