Open and Closed Maps
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In topology, an open map is a function between two topological spaces which maps open sets to open sets. That is, a function f : X Y is open if for any open set U in X, the image f(U) is open in Y. Likewise, a closed map is a function which maps closed sets to closed sets. (The concept of a closed map should not be confused with that of a closed operator.) Neither open nor closed maps are required to be continuous. Although their definitions seem natural, open and…mehr

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Produktbeschreibung
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In topology, an open map is a function between two topological spaces which maps open sets to open sets. That is, a function f : X Y is open if for any open set U in X, the image f(U) is open in Y. Likewise, a closed map is a function which maps closed sets to closed sets. (The concept of a closed map should not be confused with that of a closed operator.) Neither open nor closed maps are required to be continuous. Although their definitions seem natural, open and closed maps are much less important than continuous maps. Recall that a function f : X Y is continuous if the preimage of every open set of Y is open in X. (Equivalently, if the preimage of every closed set of Y is closed in X).