Selected Works I

bicompact spaces.- 33. Properties of the Betti groups of locally bicompact spaces.- 34. The Betti groups of metric spaces.- 35. Relative cycles. The Alexander duality theorem.- 36. On open mappings.- 37. Skew-symmetric forms and topological invariants.- 38. A study of the diffusion equation with increase in the amount of substance, and its application to a biological problem (in collaboration with I.G. Petrovskii and N.S. Piskunov).- 39. A simplified proof of the Birkhoff-Khinchin ergodic theorem.- 40. On inequalities for suprema of consecutive derivatives of an arbitrary function on an infinite interval.- 41. On rings of continuous functions on topological spaces (in collaboration with I.M. Gel'fand).- 42. Curves in a Hilbert space invariant with respect to a one-parameter group of motions.- 43. Wiener spirals and some other interesting curves in a Hilbert space.- 44. Points of local topological character of count ably-multiple open mappings of compacta.- 45. Local structure of turbulence in an incompressible viscous fluid at very large Reynolds numbers.- 46. On the degeneration of isotropic turbulence in an incompressible viscous fluid.- 47. Dissipation of energy in isotropic turbulence.- 48. Equations of turbulent motion in an incompressible fluid.- 49. A remark on Chebyshev polynomials least deviating from a given function.- 50. On the breakage of drops in a turbulent flow.- 51. On dynamical systems with an integral invariant on a torus.- 52. On the preservation of conditionally periodic motions under small variations of the Hamilton function.- 53. The general theory of dynamical systems and classical mechanics.- 54. Some fundamental problems in the approximate and exact representation of functions of one or several variables.- 55. On the representation of continuous functions of several variables as superpositions of continuous functions of a smaller number of variables.- 56. On the representation of continuous functions of several variables as superpositions of continuous functions of one variable and addition.- 57. On the linear dimension of topological vector spaces.- 58. A refinement of the concept of the local structure of turbulence in an incompressible viscous fluid at large Reynolds numbers.- 59. P.S. Aleksandrov and the theory of 8s-operations.- 60. A qualitative study of mathematical models of population dynamics.- Commentary.- List of works by A.N. Kolmogorov.