Banacha

Banacha is the genitive singular form of the Polish surname Banach. It is used in Polish to attribute properties, discoveries, or works to a person with that surname, most commonly to the Polish mathematician Stefan Banach, a central figure in functional analysis.

In mathematical terminology, objects named after Banach often bear the form Banacha, as in przestrzeń Banacha (Banach space), twierdzenie Banacha (Banach's fixed‑point theorem), and paradoks Banacha‑Tarskiego (Banach–Tarski paradox). The genitive is used to indicate association with Banach.

Stefan Banach (1892–1945) was a Polish mathematician who helped found modern functional analysis and the theory of normed spaces and linear operators. His work gave rise to many concepts that are officially labeled with his name in Polish, with Banacha appearing in their names.

The use of Banacha demonstrates how Polish language forms attach possessive references to eponymous terms, reflecting historical attribution in mathematics and science.