PreprintCC BY 4.0arXiv
Uniform Continuity of Boundary Crossing for Convex Sets
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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BibTeX
@misc{bridges2026uniform,
title = {{Uniform Continuity of Boundary Crossing for Convex Sets}},
author = {Douglas S. Bridges},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34039},
eprint = {2610.34039},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34039},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Uniform Continuity of Boundary Crossing for Convex Sets
AU - Douglas S. Bridges
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.34039
UR - https://arxiv.org/abs/2610.34039
AB - 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.
ER -