Whitney blocks in the hyperspace of a finite graph
نویسندگان
چکیده
Let X be a finite graph. Let C(X) be the hyperspace of all nonempty subcontinua of X and let μ : C(X) → R be a Whitney map. We prove that there exist numbers 0 < T0 < T1 < T2 < · · · < TM = μ(X) such that if T ∈ (Ti−1, Ti), then the Whitney block μ(Ti−1, Ti) is homeomorphic to the product μ(T )× (Ti−1, Ti). We also show that there exists only a finite number of topologically different Whitney levels for C(X).
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