leképezésre

Leképezésre is a form of the Hungarian term leképezés, with the suffix -re indicating purpose. Leképezés is a central concept in Hungarian mathematics and related fields, referring to the act or result of representing or assigning elements from one set to elements of another. In mathematics, a leképezés (often called a függvény) from a domain A to a codomain B is written as f: A → B. It describes both the rule that assigns outputs and the image f(A) contained in B. Key notions associated with leképezés include domain, codomain, image, preimage, and properties such as injectivity, surjectivity and bijectivity. Common examples include linear leképezések in linear algebra, such as f(x) = Ax from R^n to R^m, and geometric transformations like projections, rotations or reflections.

In broader usage, leképezés also denotes data mapping, image processing, or coordinate transformations in computer science and engineering. In cartography, it can describe the projection of the Earth’s surface onto a plane, i.e., a mapping from a curved surface to a plane. The terminology varies by context, but leképezés and függvény are closely related, with leképezés emphasizing the mapping relation itself and its representation.

The phrase leképezésre marks the purpose, meaning “for mapping” or “for the purpose of mapping.” It appears in expressions such as leképezésre szolgáló eljárás or ez a szoftver leképezésre van definiálva. Overall, leképezés/leképezésre denotes a fundamental concept of mapping within mathematics and its applications, spanning abstract theory to practical data transformations.