Speciality:
01.01.04 (Geometry and topology)
Birth date:
16.01.1921
Website: https://www.pdmi.ras.ru/~aaivanov Keywords: general topology; topological spaces and generalizations; topologies on one set; convergence; categorical methods; extensions of maps; function spaces; set-valued maps; extensions of spaces; sequential spaces; proximity structures; contiguity structures; uniform spaces; bitopological spaces; fixed-points.
Subject:
Scientific interests and principal results mainly concern problems of general topology. They contain creation (with V. M. Ivanova) the general theory of contiguity spaces, which quickly became classical, creation the general theory of extensions of topological spaces under minimal suppositions, the theory of topological type structures, the general theory of bitopological spaces, the theory of duality between topological structures on product $X\times Y$ and on function space $C(Y,Z)$. Outside these problems there are only some results on fixed-point theory of mappings of metric spaces and also the construction of nontrivial embeddings of cantor-discontinuum into euclidean spaces of dimension more than three.
Main publications:
Ivanova V. M., Ivanov A. A. Prostranstva smezhnosti i bikompaktnye rasshireniya topologicheskikh prostranstv // Izv. akademii nauk SSSR, seriya matematicheskaya, 1959, 23, 613–634.
Ivanov A. . Struktury rasshirenii // Zap.nauchn.semin. LOMI, 1973, t. 36, 50–125.
Ivanov A. A. Nepodvizhnye tochki otobrazhenii metricheskikh prostranstv // Zap.nauchn.semin. LOMI, 1976, t. 66, 5–102.
Ivanov A. A. Problematika teorii bitopologicheskikh prostranstv I, II, III // Zap.nauchn.semin. LOMI (POMI), 1988, 1993, 1995, t. 167, 208, 231, s. 5–62, 5–66, 9–54.
Ivanov A. A. Bitopologicheskie prostranstva // Zap.nauchn.semin. POMI, 1997, t. 242, 7–216.
