házomorfizmus

Házomorfizmus is a term originating from Hungarian mathematics, often translated as "house isomorphism" or "homeomorphism of spaces." It refers to a specific type of topological equivalence, essentially meaning that two topological spaces are the same from a topological perspective. More formally, a házomorfizmus between two topological spaces X and Y is a bijective function f: X -> Y such that both f and its inverse function f^-1 are continuous. This means that the mapping preserves the topological structure of the spaces. If a házomorfizmus exists between two spaces, they are considered topologically equivalent or homeomorphic. This concept is fundamental in topology, allowing mathematicians to classify and understand spaces based on their intrinsic properties rather than their specific embedding in a larger space. For example, a coffee mug and a donut are considered homeomorphic because one can be continuously deformed into the other without tearing or gluing. The term highlights that spaces are considered the same if they can be smoothly and reversibly transformed into one another.