open mapping

Let $X$ and $Y$ be two topological spaces. A function $f:X\to Y$ 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.

Title	open mapping
Canonical name	OpenMapping
Date of creation	2013-03-22 13:12:45
Last modified on	2013-03-22 13:12:45
Owner	Koro (127)
Last modified by	Koro (127)
Numerical id	4
Author	Koro (127)
Entry type	Definition
Classification	msc 54C10
Synonym	open function
Defines	closed function
Defines	closed mapping