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On Helly's theorem in geodesic spaces
| 1. | St. Petersburg Department of Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russian Federation |
References:
| [1] |
S. A. Bogatyĭ, The topological Helly theorem, Russian, Fundam. Prikl. Mat., 8 (2002), 365-405. |
| [2] |
M. R. Bridson and A. Haefliger, Metric Spaces of Non-Positive Curvature, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 319, Springer-Verlag, Berlin, 1999.
doi: 10.1007/978-3-662-12494-9. |
| [3] |
D. Burago and S. Ivanov, Polyhedral Finsler spaces with locally unique geodesics, Adv. Math., 247 (2013), 343-355.
doi: 10.1016/j.aim.2013.07.007. |
| [4] |
H. Busemann, Spaces with non-positive curvature, Acta Math., 80 (1948), 259-310.
doi: 10.1007/BF02393651. |
| [5] |
H. E. Debrunner, Helly type theorems derived from basic singular homology, Amer. Math. Monthly, 77 (1970), 375-380.
doi: 10.2307/2316144. |
| [6] |
B. Farb, Group actions and Helly's theorem, Adv. Math., 222 (2009), 1574-1588.
doi: 10.1016/j.aim.2009.06.004. |
| [7] |
E. Helly, Über Systeme von abgeschlossenen Mengen mit gemeinschaftlichen Punkten, Monatsh. Math. Phys., 37 (1930), 281-302.
doi: 10.1007/BF01696777. |
| [8] |
R. N. Karasev, A topological central point theorem, Topology Appl., 159 (2012), 864-868.
doi: 10.1016/j.topol.2011.12.002. |
| [9] |
B. Kleiner, The local structure of length spaces with curvature bounded above, Math. Z., 231 (1999), 409-456.
doi: 10.1007/PL00004738. |
| [10] |
B. Knaster, C. Kuratowski and S. Mazurkiewicz, Ein Beweis des Fixpunktsatzes für $n$-dimensionale Simplexe, Fund. Math., 14 (1929), 132-137. |
| [11] |
Tverberg's theorem in CAT(0) spaces, Misha, http://mathoverflow.net/users/21684,, MathOverflow, (): 2013.
|
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L. Montejano, A new topological Helly theorem, preprint, (2013). Available from: https://www.researchgate.net/publication/235626408. |
show all references
References:
| [1] |
S. A. Bogatyĭ, The topological Helly theorem, Russian, Fundam. Prikl. Mat., 8 (2002), 365-405. |
| [2] |
M. R. Bridson and A. Haefliger, Metric Spaces of Non-Positive Curvature, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 319, Springer-Verlag, Berlin, 1999.
doi: 10.1007/978-3-662-12494-9. |
| [3] |
D. Burago and S. Ivanov, Polyhedral Finsler spaces with locally unique geodesics, Adv. Math., 247 (2013), 343-355.
doi: 10.1016/j.aim.2013.07.007. |
| [4] |
H. Busemann, Spaces with non-positive curvature, Acta Math., 80 (1948), 259-310.
doi: 10.1007/BF02393651. |
| [5] |
H. E. Debrunner, Helly type theorems derived from basic singular homology, Amer. Math. Monthly, 77 (1970), 375-380.
doi: 10.2307/2316144. |
| [6] |
B. Farb, Group actions and Helly's theorem, Adv. Math., 222 (2009), 1574-1588.
doi: 10.1016/j.aim.2009.06.004. |
| [7] |
E. Helly, Über Systeme von abgeschlossenen Mengen mit gemeinschaftlichen Punkten, Monatsh. Math. Phys., 37 (1930), 281-302.
doi: 10.1007/BF01696777. |
| [8] |
R. N. Karasev, A topological central point theorem, Topology Appl., 159 (2012), 864-868.
doi: 10.1016/j.topol.2011.12.002. |
| [9] |
B. Kleiner, The local structure of length spaces with curvature bounded above, Math. Z., 231 (1999), 409-456.
doi: 10.1007/PL00004738. |
| [10] |
B. Knaster, C. Kuratowski and S. Mazurkiewicz, Ein Beweis des Fixpunktsatzes für $n$-dimensionale Simplexe, Fund. Math., 14 (1929), 132-137. |
| [11] |
Tverberg's theorem in CAT(0) spaces, Misha, http://mathoverflow.net/users/21684,, MathOverflow, (): 2013.
|
| [12] |
L. Montejano, A new topological Helly theorem, preprint, (2013). Available from: https://www.researchgate.net/publication/235626408. |
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