Mohler, Lee; Oversteegen, Lex G. On hereditarily decomposable hereditarily equivalent non-metric continua. (English) Zbl 0706.54030 Fundam. Math. 136, No. 1, 1-12 (1990). 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 Keywords:non-metric continua; hereditarily equivalent Hausdorff arcs; hereditarily decomposable, hereditarily equivalent continuum Citations:Zbl 0102.378; Zbl 0144.446; Zbl 0142.212; Zbl 0511.54019 PDFBibTeX XMLCite \textit{L. Mohler} and \textit{L. G. Oversteegen}, Fundam. Math. 136, No. 1, 1--12 (1990; Zbl 0706.54030) Full Text: DOI EuDML