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  2014, 21: 109-112. doi: 10.3934/era.2014.21.109

On Helly's theorem in geodesic spaces

Sergei Ivanov 1,

1. 

St. Petersburg Department of Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russian Federation

Received  April 2014 Published  June 2014

In this note we show that Helly's Intersection Theorem holds for convex sets in uniquely geodesic spaces (in particular, in CAT(0) spaces) without the assumption that the convex sets are open or closed.
Keywords: Helly's Theorem, covering dimension, uniquely geodesic space, CAT(0) space..
Mathematics Subject Classification: 53C23, 52A35, 54F4.
Citation: Sergei Ivanov. On Helly's theorem in geodesic spaces. Electronic Research Announcements, 2014, 21: 109-112. doi: 10.3934/era.2014.21.109
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show all references

References:
[1]

Russian, Fundam. Prikl. Mat., 8 (2002), 365-405.  Google Scholar

[2]

Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 319, Springer-Verlag, Berlin, 1999. doi: 10.1007/978-3-662-12494-9.  Google Scholar

[3]

Adv. Math., 247 (2013), 343-355. doi: 10.1016/j.aim.2013.07.007.  Google Scholar

[4]

Acta Math., 80 (1948), 259-310. doi: 10.1007/BF02393651.  Google Scholar

[5]

Amer. Math. Monthly, 77 (1970), 375-380. doi: 10.2307/2316144.  Google Scholar

[6]

Adv. Math., 222 (2009), 1574-1588. doi: 10.1016/j.aim.2009.06.004.  Google Scholar

[7]

Monatsh. Math. Phys., 37 (1930), 281-302. doi: 10.1007/BF01696777.  Google Scholar

[8]

Topology Appl., 159 (2012), 864-868. doi: 10.1016/j.topol.2011.12.002.  Google Scholar

[9]

Math. Z., 231 (1999), 409-456. doi: 10.1007/PL00004738.  Google Scholar

[10]

Fund. Math., 14 (1929), 132-137. Google Scholar

[11]

Tverberg's theorem in CAT(0) spaces, Misha, http://mathoverflow.net/users/21684,, MathOverflow, (): 2013.   Google Scholar

[12]

preprint, (2013). Available from: https://www.researchgate.net/publication/235626408. Google Scholar

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