Geodesic
Completely continuous movements in topological vector spaces
Glasgow mathematical journal, Tome 2 (1957) no. 3, pp. 135-141

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Let A be a closed subset of a topological space X and f a continuous mapping of A into X with the following two properties:1.1. f {Fr (A)} & f {Int (A)} are disjoint.1.2. The mapping f* = f | Fr (A) is 1–1.It is proved in [5], that if X is the euclidean n–sphere Sn = {x; x e Rn+1 and ― x ― = 1}, then1.3. f {Fr(A)} = Fr {f(A)}.[ Hence f{Int (A)} = Int {f(A)}]. 
Michael, J. H. Completely continuous movements in topological vector spaces. Glasgow mathematical journal, Tome 2 (1957) no. 3, pp. 135-141. doi: 10.1017/S2040618500033591
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