Sierpiskiego

Wacław Sierpiński (1882–1969) was a Polish mathematician whose work spanned set theory, topology, and number theory. A central figure in the Polish School of Mathematics, he contributed to the development of modern mathematical logic and analysis in the first half of the 20th century.

Among his most enduring contributions are several concepts that bear his name in fractal geometry and topology. The Sierpiński triangle, also called the gasket, is formed by repeatedly removing the central inverted triangle from each filled triangle, producing a self-similar set with Hausdorff dimension log 3 / log 2. A related construction is the Sierpiński carpet, built by iteratively removing central subsquares from a square grid, with Hausdorff dimension log 8 / log 3.

In topology, the Sierpiński space is a simple two-point topological space used as a textbook counterexample to illustrate basic separation and continuity concepts.

In set theory and measure theory, he introduced the notion of a Sierpiński set, a subset of the real numbers that intersects every Lebesgue measure zero set in a countable set. The existence of such sets is independent of ZFC and is often discussed under the Continuum Hypothesis.

In number theory, Sierpiński studied problems related to primes and composite forms; a Sierpiński number is an odd integer k for which k·2^n + 1 is composite for every positive integer n.

His work left a lasting impact on multiple branches of mathematics, and his name is attached to several standard constructions and counterexamples.