leképezést

Leképezést is a Hungarian term that translates to "mapping" or "representation" in English. In various fields, it refers to the process of establishing a correspondence or relationship between elements of one set or space and elements of another. This concept is fundamental in mathematics, particularly in abstract algebra, geometry, and analysis.

In mathematics, a leképezést can describe a function that takes an input from a domain and produces an output in a codomain. For example, a linear transformation is a type of leképezést that preserves vector addition and scalar multiplication. Geometric leképezések include transformations like translations, rotations, and reflections, which alter the position or orientation of geometric objects. In set theory, a leképezést is a function that maps elements from one set to another, indicating a relationship between these sets.

Beyond pure mathematics, the term leképezést can be used in more general contexts. In computer science, it might refer to data mapping, where data from one format is transformed into another. In cartography, a map is a leképezést of a portion of the Earth's surface onto a two-dimensional plane. The core idea remains consistent: establishing a defined way to connect or represent elements from one entity to another, often simplifying or abstracting complex relationships.