Definition:Open Mapping

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Let $\struct {S_1, \tau_1}$ and $\struct {S_2, \tau_2}$ be topological spaces.

Let $f: S_1 \to S_2$ be a mapping.

Then $f$ is said to be an open mapping if and only if:

$\forall U \in \tau_1: f \sqbrk U \in \tau_2$

where $f \sqbrk U$ denotes the image of $U$ under $f$.


This is not to be confused with the concept of $f$ being continuous.

Also see

  • Results about open mappings can be found here.