Equivalent conditions to a map being a quotient map

From Maths
Jump to: navigation, search
Stub grade: A
This page is a stub
This page is a stub, so it contains little or minimal information and is on a to-do list for being expanded.The message provided is:
Review and demote
Note: this page will have to be re-written if other conditions are to be added.


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 and only if

  • It does either one, or both, of the following:
    1. [ilmath]f[/ilmath] takes saturated open sets to open sets
    2. [ilmath]f[/ilmath] takes saturated closed sets to closed sets


Grade: A
This page requires one or more proofs to be filled in, it is on a to-do list for being expanded with them.
Please note that this does not mean the content is unreliable. Unless there are any caveats mentioned below the statement comes from a reliable source. As always, Warnings and limitations will be clearly shown and possibly highlighted if very important (see template:Caution et al).
The message provided is:
Unfortunately left as an exercise


  1. Introduction to Topological Manifolds - John M. Lee