On the Inverse Limit of Euclidean Tv-sphereso
نویسنده
چکیده
In [l] Bing constructed a 1-dimensional hereditarily indecomposable continuum which is the inverse limit of a sequence of circles Ct and such that the maps/*: C —>C;_i were of degree 1. In this paper we show that the dimension cannot be raised, i.e., if 5 = Lim(54 , /,-) where St is an TV-sphere and fi is essential, then 5 is not hereditarily indecomposable. In doing so we further generalize Bing's definition of "e-crooked." Lemma 2 shows how to construct hereditarily indecomposable continua by making the bonding maps sufficiently crooked. In Lemma 3 we get a necessary crookedness condition on the bonding maps if the limit space is to be hereditarily indecomposable. The remainder of the paper is devoted to proving that in the case of TV-spheres (TV>1) this condition cannot be satisfied. Definitions and Notation. Let Xi he a sequence of compact metric spaces, and for i^2 let/,be a map of Xt into _T*_i. Then the subspace(2)(3)
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