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.
 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.
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