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In mathematics, even more specifically in geography, an open map is a function in between 2 topological areas that maps open collections to open sets. That is, a feature f. :. X. →. Y. is open if for any type of open collection. U. in. X. ,. \ displaystyle X, the picture. f. (. U. ). \ displaystyle f( U) is open in. Y . Furthermore, a closed map is a function that maps closed collections to shut sets. A map might be open, closed, both, or neither; in certain, an open map need not be closed and also vice versa.Open and also closed maps are not always continuous. Additionally, continuity is independent of openness and also closedness in the basic instance and a continuous feature may have one, both, or neither building; this truth remains real also if one limits oneself to metric areas. Although their definitions appear even more all-natural, open as well as shut maps are a lot lesser than constant maps. Recall that, by definition, a function. f. :. X. →. Y. \ displaystyle f:...