Hausdorff, Felix (1868-1942)

German mathematician and philosopher who developed the branch of mathematics known as topology, in which he formulated the theory of point sets. He investigated general closure spaces, and formulated Hausdorff's maximal principle in general set theory.

Hausdorff was born in Breslau, Germany (now Wrocław, Poland), and studied at Berlin, Freiburg, and Leipzig. In 1902 he was appointed professor at Leipzig, later moving to Bonn. During World War II he committed suicide rather than be sent to a concentration camp.

Hausdorff formulated a theory of topological and metric spaces, proposing that such spaces be regarded as sets of points and sets of relations among the points, and introduced the principle of duality. This principle states that an equation between sets remains valid if the sets are replaced by their complements and the symbol for union is exchanged for that of intersection.

He also created what are now called Hausdorff's neighbourhood axioms; from these four axioms he derived Hausdorff's topological spaces. A topological space is understood to be a set E of elements x and certain subsets Sx of E which are known as neighbourhoods of x.

Hausdorff also contributed extensively to several other fields of mathematics.

His major work is Grundzuge der Mengenlehre/Basic Features of Set Theory (1914).