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arXiv · 2610.34039

Uniform Continuity of Boundary Crossing for Convex Sets

Douglas S. Bridges
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Abstract

Let C be an inhabited, bounded, open, convex subset of a Banach space, and phi the pointwise continuous mapping taking a pair of points, one inside C and one outside, to the point where the segment joining those points meets the boundary of C. We prove constructively that phi is uniformly continuous on the Cartesian product of a set well contained in C and the metric complement of C.

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Douglas S. Bridges. 2026-10-25. Uniform Continuity of Boundary Crossing for Convex Sets. https://arxiv.org/abs/2610.34039

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