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