In 1985 M. Smith constructed a nonmetric pseudo-arc; i.e. a Hausdorff homogeneous, hereditary equivalent and hereditary indecomposable continuum. Taking advantage of a decomposition theorem of W. Lewis, he obtained it as a long inverse limit of metric pseudo-arcs with monotone bonding maps. Extending his approach, and the results of Lewis on lifting homeomorphisms, we construct a nonmetric pseudo-circle, and new examples of homogeneous 1-dimensional continua; e.g. a circle and solenoids of nonmetric pseudo-arcs. Among many corollaries we also obtain an analogue of another theorem of Lewis from 1984: any interval map is semi-conjugate to a homeomorphism of the nonmetric pseudo-arc.

中文翻译：

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非度量伪弧和半共轭到区间映射的连续曲线

1985 年，M. Smith 构造了一个非度量伪弧；即 Hausdorff 同质、遗传等价和遗传不可分解的连续统。利用 W. Lewis 的分解定理，他得到了它作为具有单调键合映射的度量伪弧的长逆极限。扩展他的方法，以及刘易斯在提升同胚方面的结果，我们构建了一个非度量伪圆，以及齐次一维连续体的新例子；例如，非度量伪弧的圆和螺线管。在许多推论中，我们还得到了 1984 年路易斯的另一个定理的类似物：任何区间映射与非度量伪弧的同胚半共轭。