PlanetMath: open mapping

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open mapping

(Definition)

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

Accordingly, if is closed for each closed subset of , we say that 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:

54C10 (General topology :: Maps and general types of spaces defined by maps :: Special maps on topological spaces )

Pending Errata and Addenda

None.

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