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 { X i } i = 0 2 be any family of simply connected compact subsets of R 2 such that for every i , j ∈ { 0 , 1 , 2 } the intersections X i ∩ X j are path connected and ⋂ i = 0 2 X i is nonempty. Then for every two points in the intersection ⋂ i = 0 2 X i there exists a cell-like compactum connecting these two points, in particular the intersection ⋂ i = 0 2 X i is a connected set.
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