Definitions for "Homeomorphism"
A 1-to-1 mapping between topological spaces that preserves the topological structure, i. e. the open sets. Homeomorphic spaces have essentially the same topological properties.
If ''X'' and ''Y'' are spaces, a homeomorphism from ''X'' to ''Y'' is a bijective function ''f'' : ''X'' → ''Y'' such that ''f'' and ''f''−1 are continuous. The spaces ''X'' and ''Y'' are then said to be homeomorphic. From the standpoint of topology, homeomorphic spaces are identical.
A one-to-one continuous transformation that preserves open and closed sets.