Editing Felix Hausdorff (section)

===His last works===
In 1938, Hausdorff's last work ''Extension of a continuous map'' showed that a [[continuous function]] from a closed subset <math>F</math> of a metric space <math>E</math> can be extended to all of <math>E</math> (although the image may need to be extended). As a special case, every [[homeomorphism]] from <math>F</math> can be extended to a homeomorphism from <math>E</math>. This work continued research from earlier years. In 1919, in ''About semi-continuous functions and their generalization'', Hausdorff had, among other things, given another proof of the [[Tietze extension theorem]]. In 1930, in ''Extending a homeomorphism'', he showed the following: Let <math>E</math> be a metric space, <math>F \subseteq E</math> a closed subset. If <math>F</math> is given a new metric without changing the topology, this metric can be extended to the entire space without changing the topology. The work ''Graded spaces'' appeared in 1935, where Hausdorff discussed spaces which fulfilled the [[Kuratowski closure axioms]] up to the axiom of idempotence. These spaces are often also called closure spaces, and Hausdorff used them to study relationships between the [[Maurice René Fréchet|Fréchet]] limit spaces and [[topological spaces]].