Open, convex, unbounded sets in normed spaces
Functional Analysis
2017-10-31 v1
Abstract
Let X be a normed linear space. We examine if every open, convex and unbounded subset of X is equal to the union of a family of open straight half lines. The answer is affirmative if and only if X is finite dimensional.
Cite
@article{arxiv.1710.10656,
title = {Open, convex, unbounded sets in normed spaces},
author = {D. Moshonas and V. Nestoridis and A. Terezakis},
journal= {arXiv preprint arXiv:1710.10656},
year = {2017}
}
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8 pages, 0 figures