Abstract
A function ƒ: R n→ R n, n⩾2 , is sectionally continuous if each restriction ƒ| H to an ( n − 1)-dimensional hyperplane H is continuous. We show that a sectionally continuous injection ƒ is continuous at a point x in R n if and only if ƒ(x) is not a limit point of any component of R nƒ( R n) . In particular, ƒ is an imbedding if and only if ƒ( R n) is open. For n = 2, we also describe all possible images for sectionally continuous injections with only countably many discontinuities.
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