Menger became interested in the topic and was encouraged by Hahn to work on the topic. Menger's work led him to a definition of dimension independently of Urysohn, however Urysohn had died in a drowning accident before he could publish his work and Menger was not aware of it.
Menger naging interesado sa paksa at ay hinihikayat sa pamamagitan ng Hahn sa trabaho sa paksa. Menger ng trabaho sa kanya na humantong sa isang kahulugan ng laki na malaya ng Urysohn, subalit Urysohn may namatay sa isang aksidente nabubuwal bago siya ay mai-publish ang kanyang trabaho at Menger ay hindi alam ng mga ito.