• Source: Topological abelian group

In mathematics, a topological abelian group, or TAG, is a topological group that is also an abelian group.
That is, a TAG is both a group and a topological space, the group operations are continuous, and the group's binary operation is commutative.
The theory of topological groups applies also to TAGs, but more can be done with TAGs. Locally compact TAGs, in particular, are used heavily in harmonic analysis.




See also


Compact group – Topological group with compact topology
Complete field – algebraic structure that is complete relative to a metricPages displaying wikidata descriptions as a fallback
Fourier transform – Mathematical transform that expresses a function of time as a function of frequency
Haar measure – Left-invariant (or right-invariant) measure on locally compact topological group
Locally compact field
Locally compact quantum group – relatively new C*-algebraic approach toward quantum groupsPages displaying wikidata descriptions as a fallback
Locally compact group – topological group for which the underlying topology is locally compact and Hausdorff, so that the Haar measure can be definedPages displaying wikidata descriptions as a fallback
Pontryagin duality – Duality for locally compact abelian groups
Protorus – Mathematical object, a topological abelian group that is compact and connected
Ordered topological vector space
Topological field – Algebraic structure with addition, multiplication, and divisionPages displaying short descriptions of redirect targets
Topological group – Group that is a topological space with continuous group action
Topological module
Topological ring – ring where ring operations are continuousPages displaying wikidata descriptions as a fallback
Topological semigroup – semigroup with continuous operationPages displaying wikidata descriptions as a fallback
Topological vector space – Vector space with a notion of nearness




References



Banaszczyk, Wojciech (1991). Additive subgroups of topological vector spaces. Lecture Notes in Mathematics. Vol. 1466. Berlin: Springer-Verlag. pp. viii+178. ISBN 3-540-53917-4. MR 1119302.
Fourier analysis on Groups, by Walter Rudin.

Kata Kunci Pencarian:

• Grup abelian bebas
• Subgrup komutator
• Ekstensi grup
• Grup (matematika)
• Grup dasar
• Lapangan (matematika)
• Daftar masalah matematika yang belum terpecahkan
• Topological abelian group
• Topological group
• Locally compact group
• Pontryagin duality
• Locally compact abelian group
• Topological ring
• Pre-abelian category
• Modes of convergence
• Discrete group
• Extension of a topological group