## Encyclopaedia of Mathematics, Volume 4This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques. |

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1980 Subject Classification Abelian group Acad algebra Amer AMS 1980 Subject analysis analytic functions arbitrary axioms Banach Banach space boundary calculus called coefficients cohomology compact complex computation concept condition connected construction converges coordinates corresponding curvature curve defined denoted differential equations dimension dimensional domain Editorial comments elements Euclidean Euclidean space example exists field finite group formal formula Fourier series fractional-linear mapping Fredholm func functor G-structure Galois Gauss geodesic geometry given grammar graph group G harmonic Hermitian Hilbert space homogeneous homogeneous space homology groups homomorphism homotopy integral invariant isomorphic language Lie group linear manifold mapping Math mathematical matrix method metric module morphism Nauk obtained operator polynomials problem properties References A1 representation respect Riemann Riemannian ring Russian scheme sequence solution Springer structure subgroup subset surface theorem theory tion topological space transformations translated Univ values variables vector space vertices