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# Edward Marczewski

Edward Marczewski (15 November 1907 in Warsaw, Congress Poland, Russian Empire - 17 October 1976 in Wrocław, Poland) was a Polish mathematician. His surname until 1940 was Szpilrajn.

Marczewski was a member of the Warsaw School of Mathematics. 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, general topology, probability theory and universal algebra. 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 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).[1] This is a fundamental theorem of fractal theory. (Certain contributions to this development were also made by Samuel Eilenberg, see: Witold Hurewicz and Henry Wallman, Dimension Theory, 1941, Chapter VII.)

See also

* Szpilrajn extension theorem

* Marczewski function

References

1. ^ E. Szpilrajn (1937). La dimension et la mesure, Fund. Math. 28, pp 81-89

External links

* O'Connor, John J.; Robertson, Edmund F., "Edward Marczewski", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Marczewski.html .

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