On the topological Helly theorem |
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Authors: | Umed H Karimov |
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Institution: | a Institute of Mathematics, Academy of Sciences of Tajikistan, ul. Ainy 299A, Dushanbe 734063, Tajikistan b Institute of Mathematics, Physics and Mechanics, University of Ljubljana, PO Box 2964, Ljubljana 1001, Slovenia |
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Abstract: | The main result of this paper is the following theorem, related to the missing link in the proof of the topological version of the classical result of Helly: Let be any family of simply connected compact subsets of R2 such that for every i,j∈{0,1,2} the intersections Xi∩Xj are path connected and is nonempty. Then for every two points in the intersection there exists a cell-like compactum connecting these two points, in particular the intersection is a connected set. |
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Keywords: | primary 54F15 55N10 secondary 54D05 |
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