Difference between revisions of "Open map"

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==Definition==
 
==Definition==

Latest revision as of 22:53, 22 February 2017

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Created quickly, just to document the concept
A closed map is a thing too and is defined similarly.

Definition

Let (X,J) and (Y,K) be topological spaces and let f:XY be a map (not necessarily continuous - just a map between X and Y considered as sets), then we call f an open map if[1]:

  • UJ[f(U)K] - that is, that the images (under f) of all open sets of (X,J) are open in (Y,K)

References

  1. Jump up Introduction to Topological Manifolds - John M. Lee