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

• Fourier transform
• Haar measure
• Pontryagin duality
• Protorus, a topological abelian group that is compact and connected

References

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