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open mapping (Definition)

Let $ X$ and $ Y$ be two topological spaces. A function $ f:X\rightarrow Y$ is said to be open if $ f(U)$ is open for each open subset $ U$ of $ X$.

Accordingly, if $ f(C)$ is closed for each closed subset $ C$ of $ X$, we say that $ f$ is closed.



"open mapping" is owned by Koro.
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Other names:  open function
Also defines:  closed function, closed mapping

Attachments:
continuous surjective open maps in terms of nets (Theorem) by asteroid
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Cross-references: closed subset, closed, open subset, open, function, topological spaces
There are 7 references to this entry.

This is version 1 of open mapping, born on 2002-12-07.
Object id is 3676, canonical name is OpenMapping.
Accessed 5617 times total.

Classification:
AMS MSC54C10 (General topology :: Maps and general types of spaces defined by maps :: Special maps on topological spaces )

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