Difference between revisions of "Task:Equivalent properties to homeomorphism"

Latest revision as of 20:25, 26 September 2016

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:
  1. [ilmath]f[/ilmath] is a homeomorphism
  2. [ilmath]f[/ilmath] is an open map
  3. [ilmath]f[/ilmath] is a closed map

References

1. ↑ Introduction to Topological Manifolds - John M. Lee