| 31. | Since the transformations depend continuously on, is a continuous group, also called a topological group.
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| 32. | It is in this form that the regular representation is generalized to topological groups such as Lie groups.
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| 33. | This relationship generalizes to the idea of Tannaka-Krein duality between compact topological groups and their representations.
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| 34. | The Bohr compactification is intimately connected to the finite-dimensional unitary representation theory of a topological group.
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| 35. | Automorphic forms are a generalization of the idea of periodic functions in Euclidean space to general topological groups.
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| 36. | In every Banach algebra with multiplicative identity, the set of invertible elements forms a topological group under multiplication.
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| 37. | The uniform structures allow one to talk about notions such as uniform continuity and uniform convergence on topological groups.
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| 38. | A solenoid is a one-dimensional homogeneous indecomposable continuum that has the structure of a compact topological group.
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| 39. | R�dstr�m was interested in Hilbert's fifth problem on the analyticity of the continuous operation of topological groups.
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| 40. | For example, the structure of a topological group consists of a topology and the structure of a group.
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