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On hereditarily decomposable hereditarily equivalent non-metric continua. (English) Zbl 0706.54030

Summary: We give a method for constructing hereditarily equivalent Hausdorff arcs. The method yields four topologically distinct examples, two of which are known and two new. An example is given of a hereditarily decomposable, hereditarily equivalent continuum which is not an arc. This example shows that theorems of G. W. Henderson [Ann. Math., II. Ser. 72, 421-428 (1960; Zbl 0102.378)], W. S. Mahavier [Fundam. Math. 60, 53-57 (1967; Zbl 0144.446)] and E. S. Thomas jun. [Diss. Math. 50 (1966; Zbl 0142.212)] and L. G. Oversteegen and E. D. Tymchatyn [Tran. Am. Math. Soc. 278, 717-724 (1983; Zbl 0511.54019)] will not generalize to the non-metric setting.

MSC:

54F15 Continua and generalizations
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