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By using some simple tools from graph theory, we obtain a characterization of the compact sets in $$\mathbb {R}^n$$ with Borsuk number equal to two. This result allows to give… Click to show full abstract
By using some simple tools from graph theory, we obtain a characterization of the compact sets in $$\mathbb {R}^n$$ with Borsuk number equal to two. This result allows to give some examples of planar (convex) compact sets with Borsuk number equal to three. Moreover, we also prove that the unique centrally symmetric planar convex compact sets with Borsuk number equal to three are the Euclidean balls.
Keywords:
borsuk number;
number equal;
number;
planar convex;
compact sets
Journal Title: Results in Mathematics
Year Published: 2019
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Journal Title: Results in Mathematics
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!