 ##  [Homeomorphism](/homeomorphism) 

  ##  [Homeomorphism](https://natural.quantumdictionary.io/homeomorphism-0) 

  
 [![Natural & Formal Sciences Dictionary](/sites/default/files/styles/large/public/2026-01/Natural%20%26%20Formal%20Sciences.png.webp?itok=2kCDRVQv)](/topic-specific-dictionaries/natural-formal-sciences)


**Natural &amp; Formal Sciences Dictionary**

 
Definition

A bijective continuous map between topological spaces that has a continuous inverse, establishing a topological equivalence between the spaces.

 
 ##  [Homeomorphism](https://mathlogic.quantumdictionary.io/homeomorphism-1) 

  
 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural &amp; Formal Sciences -

**Mathematics &amp; Logic Dictionary**

 
Definition

A continuous bijection between two topological spaces whose inverse is also continuous; it establishes a topological equivalence that preserves open sets, continuity properties, and topological invariants.

 
 ##  [Homeomorphism](https://puremath.quantumdictionary.io/homeomorphism-2) 

  
 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics &amp; Logic -

**Pure Mathematics Dictionary**

 
Definition

A bijective continuous map between topological spaces whose inverse is also continuous; it is the isomorphism notion in the category of topological spaces and identifies spaces that are topologically the same.