# Task:Equivalent properties to homeomorphism

From Maths

## Task

Fit the following into the main wiki

## Statement

Let [ilmath](X,\mathcal{ J })[/ilmath] and [ilmath](Y,\mathcal{ K })[/ilmath] be topological spaces and let [ilmath]f:X\rightarrow Y[/ilmath] be a map. Then^{[1]}:

- If [ilmath]f[/ilmath] is a bijective and continuous map, the following are equivalent:
- [ilmath]f[/ilmath] is a homeomorphism
- [ilmath]f[/ilmath] is an open map
- [ilmath]f[/ilmath] is a closed map

## References