TSSFL TECHNOLOGY STACK

In the mathematical field of topology, a homeomorphism or topological isomorphism or bi continuous function is a continuous function between topological spaces that has a continuous inverse function.

Formally,

A function between two topological spaces and is called a homeomorphism if it has the following properties:

• is a bijection (one-to-one and onto),
• is continuous,
• the inverse function is continuous ( is an open mapping).

A function with these three properties is sometimes called bicontinuous. If such a function exists, we say and are homeomorphic. A self-homeomorphism is a homeomorphism of a topological space and itself. The homeomorphisms form an equivalence relation on the class of all topological spaces. The resulting equivalence classes are called homeomorphism classes.

A continuous deformation between a coffee mug and a donut (torus) illustrating that they are homeomorphic ( a continuous mapping with a continuous inverse function ).

What is holomorphic function?