Edward Marczewski was a Polish

Poland

Poland , officially the Republic of Poland , is a country in Central Europe bordered by Germany to the west; the Czech Republic and Slovakia to the south; Ukraine, Belarus and Lithuania to the east; and the Baltic Sea and Kaliningrad Oblast, a Russian exclave, to the north...

 mathematician

Mathematician

A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

. His surname until 1940 was Szpilrajn.

Marczewski was a member of the Warsaw School of Mathematics

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 published in the journal Fundamenta Mathematicae, founded...

. His life and work after the Second World War were connected with Wrocław, where he was among the creators of the Polish scientific centre.

Marczewski's main fields of interest were measure theory, descriptive set theory

Descriptive set theory

In mathematical logic, descriptive set theory is the study of certain classes of "well-behaved" subsets of the real line and other Polish spaces...

, general topology

General topology

In mathematics, general topology or point-set topology is the branch of topology which studies properties of topological spaces and structures defined on them...

, probability theory

Probability theory

Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...

 and universal algebra

Universal algebra

Universal algebra is the field of mathematics that studies algebraic structures themselves, not examples of algebraic structures....

. He also published papers on real and complex analysis, applied mathematics and mathematical logic.

Marczewski proved that the topological dimension, for arbitrary metrisable separable space X, coincides with the Hausdorff dimension

Hausdorff dimension

thumb|450px|Estimating the Hausdorff dimension of the coast of Great BritainIn mathematics, the Hausdorff dimension is an extended non-negative real number associated with any metric space. The Hausdorff dimension generalizes the notion of the dimension of a real vector space...

 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. (Certain contributions to this development were also made by Samuel Eilenberg

Samuel Eilenberg

Samuel Eilenberg was a Polish and American mathematician of Jewish descent. He was born in Warsaw, Russian Empire and died in New York City, USA, where he had spent much of his career as a professor at Columbia University.He earned his Ph.D. from University of Warsaw in 1936. His thesis advisor...

, see: Witold Hurewicz

Witold Hurewicz

Witold Hurewicz was a Polish mathematician.- Early life and education :Witold Hurewicz was born to a Jewish family in Łódź, Russian Empire ....

 and Henry Wallman

Henry Wallman

Henry Wallman was an American mathematician, known for his work in lattice theory, dimension theory, topology, and electronic circuit design.A native of Brooklyn and a 1933 graduate of Brooklyn College, Wallman received his Ph.D...

, Dimension Theory, 1941, Chapter VII.)

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