He is most famous for applying the topological concept of retract, introduced by Karol Borsuk, to the study of the solutions of differential equations.

Ważewski went to, originally, study physics at the Jagiellonian University (Krakow), but after being convinced by Stanisław Zaremba, he would change his degree to mathematics.

Then in 1927 he was awarded the Habilitation at the Jagiellonian University on the basis of the thesis Rectifiable Continuums in Relation to Absolutely Continuous Functions and Mappings (Polish).

[4] In the years after his Habilitation he continued to work at the Jagiellonian University but his focus had moved from topology to analysis.

[1] During World War II Ważewski was taken to the Sachsenhausen-Oranienburg concentration camp where he would be kept until his release in February 1940.