View source for Open map

{{Stub page|grade=B|msg=Created quickly, just to document the concept}}
: A [[closed map]] is a thing too and is defined similarly. 
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==Definition==
Let {{Top.|X|J}} and {{Top.|Y|K}} be [[topological spaces]] and let {{M|f:X\rightarrow Y}} be a [[map]] (not necessarily [[continuous]] - just a map between {{M|X}} and {{M|Y}} considered as sets), then {{nowrap|we call {{M|f}} an ''open map'' if{{rITTMJML}}}}:
* {{M|1=\forall U\in\mathcal{J}[f(U)\in\mathcal{K}]}} - that is, that the {{link|image|map|s}} (under {{M|f}}) of all {{plural|open set|s}} of {{Top.|X|J}} are [[open set|open]] in {{Top.|Y|K}}
==References==
<references/>
{{Definition|Topology}}