Open map
In general topology, an open map is a function from a topological space (the domain) to (the same or another) topological space (the codomain) that maps every open set in the domain to an open set in the codomain.
A homeomorphism may be defined as a continuous open bijection.
[edit] Open mapping theorem
The open mapping theorem states that under suitable conditions a differentiable function may be an open map.
Open mapping theorem for real functions. Let f be a function from an open domain D in Rn to Rn which is continuously differentiable and has non-singular derivative (in other words, non-zero Jacobian) in D. Then f is an open map on D.
Open mapping theorem for complex functions. Let f be a non-constant holomorphic function on an open domain D in the complex plane. Then f is an open map on D.
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