Homeomorphism
Geometry and topology
A continuous one-to-one correspondence between two spaces whose inverse is also continuous. Spaces related by one are topologically identical.
What is usually left out
Requiring the inverse to be continuous is not redundant. The map wrapping a half-open interval around a circle is continuous and one-to-one onto the circle, but its inverse tears the circle apart, so the two are not homeomorphic — as they should not be.