ALEXANDROFF 8 



Gottingen Academy of Sciences (1929-38, and from 1945), the 

 Polish Academy of Sciences and other societies. In 1943 he 

 was awarded a Stalin Prize. 



Alexandroff investigated the theory of point sets and the 

 theory of the function of the real variable, obtaining such im- 

 portant results as the proof of the theorem on the power of 

 Borel sets. In collaboration with P. S. Urysohn he developed in 

 the Soviet Union the field of topology, becoming the head of the 

 U.S.S.R. School of Topology. Among his former students are: 

 L. Pontryagin, A. Tychonoff, A. Kurosh, Yu. Smirnov, G. 

 Chogoshvili, K. Sitnikov and others. Alexandroff originated one 

 of the main theories of topological spaces—the theory of bi- 

 compact spaces. He also contributed in an essential way to the 

 modern theory of dimensionality (in particular he founded the 

 theory of the homogical dimension); he was the founder of 

 methods based on combinatory algebraic investigation of sets 

 and spaces of a general nature; he proved a series of basic 

 "laws of duality" (combining topological properties of the geo- 

 metrical figure with topological properties of space comple- 

 mentary to it). 

 Bibliography: 



Sur la puissance des ensembles mesurables B. Comptes 

 Rendus Acad. Sci. Paris, 1916, 162, p. 323. 

 and P. Urysohn . Une condition necessaire et suffisante pour 

 qu'une classe (L) soit une classe (D). Compt. Rend. Acad. 

 Paris, 1923, 177, p. 1274. 



Ueber die Aequivalenz des Perronschen und des Denjoyschen 

 Integralbegriffes, Math. Zeitschrift 1924, 20, p. 213. 

 Les ensembles de premiere classe et les espaces abstraits. 

 Compt. Rend. Acad. Paris, 1924, 178, p. 185. 

 and P. Urysohn . Memoire sur les espaces topologiques 

 compacts. Verhandelingen Kon. Acad. Amsterdam, 1929, 

 14:1, p. 1. 



Untersuchungen iiber Gestalt und Lage abgeschlossener 

 Mengen beliebiger Dimension. Annals of Math., 1929, 30, 

 p. 101. 



Dimensions theorie. Ein Beitrag zur Geometrie der abge- 

 schlossener Mengen. Mathematische Annalen, 1932, 106 , 

 p. 161. 



On local properties of closed sets. Annals of Math., 1935, 

 36, p. 1. 



On bicompact extensions of topological spaces. Matemati- 

 ceski Sbornik, 1939, 5, p. 403. 



