Abstract
The Chogoshvili Claim states that for each k-dimensional compactum X in R n , there exists an ( n − k)-plane P in R n such that X is not removable from P. This means that for some ε > 0, every map f : X → R n with ∥ x − f ( x)∥ < ε for all x ϵ X, has the property that f( X) ∩ P ≠ φ. A counterexample to this claim has recently been constructed by A. Dranishnikov. Our results show, among other things, that each 2-dimensional LC 1 compactum, and hence each 2-dimensional disk, obeys the claim. To help indicate the sharpness of the preceding, we also provide a local path-connectification of Dranishnikov's example.
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