Edward Marczewski (15 November 1907 – 17 October 1976) was a Polish

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

. He was born Szpilrajn but changed his name while hiding from Nazi persecution. Marczewski was a member of the

Warsaw School of Mathematics Warsaw School of Mathematics is the name given to a group of mathematicians who worked at Warsaw, Poland, in the two decades between the World Wars, especially in the fields of logic, set theory, point-set topology and real analysis. They publishe ...

. His life and work after the

Second World War World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...

were connected with

Wrocław Wrocław (; german: Breslau, or . ; Silesian German: ''Brassel'') is a city in southwestern Poland and the largest city in the historical region of Silesia. It lies on the banks of the River Oder in the Silesian Lowlands of Central Europe, rou ...

, where he was among the creators of the Polish scientific centre. Marczewski's main fields of interest were

measure theory In mathematics, the concept of a measure is a generalization and formalization of geometrical measures ( length, area, volume) and other common notions, such as mass and probability of events. These seemingly distinct concepts have many simil ...

descriptive set theory In mathematical logic, descriptive set theory (DST) is the study of certain classes of "well-behaved" subsets of the real line and other Polish spaces. As well as being one of the primary areas of research in set theory, it has applications to ot ...

general topology In mathematics, general topology is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology. It is the foundation of most other branches of topology, including differential topology, geomet ...

probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set o ...

and

universal algebra Universal algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures themselves, not examples ("models") of algebraic structures. For instance, rather than take particular groups as the object of study, ...

. He also published papers on real and complex analysis, applied mathematics and mathematical logic. Marczewski proved that the

topological dimension In mathematics, the Lebesgue covering dimension or topological dimension of a topological space is one of several different ways of defining the dimension of the space in a topological invariant, topologically invariant way. Informal discussion F ...

, for arbitrary

metrisable In topology and related areas of mathematics, a metrizable space is a topological space that is Homeomorphism, homeomorphic to a metric space. That is, a topological space (X, \mathcal) is said to be metrizable if there is a Metric (mathematics), m ...

separable space In mathematics, a topological space is called separable if it contains a countable, dense subset; that is, there exists a sequence \_^ of elements of the space such that every nonempty open subset of the space contains at least one element of the ...

''X'', coincides with the

Hausdorff dimension In mathematics, Hausdorff dimension is a measure of ''roughness'', or more specifically, fractal dimension, that was first introduced in 1918 by mathematician Felix Hausdorff. For instance, the Hausdorff dimension of a single point is zero, of a ...

under one of the metrics in ''X'' which induce the given topology of ''X'' (while otherwise the Hausdorff dimension is always greater or equal to the topological dimension). This is a fundamental theorem of

fractal theory In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illus ...

. (Certain contributions to this development were also made by

Samuel Eilenberg Samuel Eilenberg (September 30, 1913 – January 30, 1998) was a Polish-American mathematician who co-founded category theory (with Saunders Mac Lane) and homological algebra. Early life and education He was born in Warsaw, Kingdom of Poland to a ...

, see:

Witold Hurewicz Witold Hurewicz (June 29, 1904 – September 6, 1956) was a Polish mathematician. Early life and education Witold Hurewicz was born in Łódź, at the time one of the main Polish industrial hubs with economy focused on the textile industry. His ...

and

Henry Wallman Henry "Hank" Wallman (1915Biography of Wallman ...

, ''Dimension Theory'', 1941, Chapter VII.)

References

External links

* * 1907 births 1976 deaths 20th-century Polish Jews Warsaw School of Mathematics People from Warsaw Governorate University of Warsaw alumni Academic staff of the University of Wrocław {{Poland-mathematician-stub