Suns are convex in tangent directions
Keyword(s):
A direction d is called a tangent direction to the unit sphere S of a normed linear space s S and lin(s + d) is a tangent line to the sphere S at s imply that lin(s + d) is a one-sided tangent to the sphere S, i. e., it is the limit of secant lines at s. A set M is called convex with respect to a direction d if [x, y] M whenever x, y in M, (y - x) || d. We show that in a normed linear space an arbitrary sun (in particular, a boundedly compact Chebyshev set) is convex with respect to any tangent direction of the unit sphere.
2014 ◽
Vol 98
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pp. 161-231
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1969 ◽
Vol 10
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pp. 68-72
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2020 ◽
Vol 12
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1972 ◽
Vol 13
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pp. 167-170
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2017 ◽
Vol 13
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pp. 123-134
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