Abstract
In this paper the equivalence of tree-like and cellular is proved for 1 1 -dimensional continua in E n {E^n} . More precisely, if X X is a tree-like continuum, then the collection of all embeddings h : X → E n , n ≧ 3 h:X \to {E^n},n \geqq 3 , such that h [ X ] h[X] is cellular in E n {E^n} is a dense G δ {G_\delta } -subset of the collection of all maps from X X into E n {E^n} . Conversely, if X X is a 1 1 -dimensional cellular subset of E n {E^n} , then X X is a tree-like continuum.
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