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
- {{annotated link|Compact group}}
- {{annotated link|Complete field}}
- {{annotated link|Fourier transform}}
- {{annotated link|Haar measure}}
- {{annotated link|Locally compact field}}
- {{annotated link|Locally compact quantum group}}
- {{annotated link|Locally compact group}}
- {{annotated link|Pontryagin duality}}
- {{annotated link|Protorus}}, a topological abelian group that is compact and connected
- {{annotated link|Ordered topological vector space}}
- {{annotated link|Topological field}}
- {{annotated link|Topological group}}
- {{annotated link|Topological module}}
- {{annotated link|Topological ring}}
- {{annotated link|Topological semigroup}}
- {{annotated link|Topological vector space}}
References
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- {{cite book|last=Banaszczyk|first=Wojciech|title=Additive subgroups of topological vector spaces|series=Lecture Notes in Mathematics|volume=1466|publisher=Springer-Verlag|location=Berlin|year= 1991|pages=viii+178|isbn=3-540-53917-4|mr=1119302}}
- Fourier analysis on Groups, by Walter Rudin.
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