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On non-metric continua that support Whitney maps

机译：在支持惠特尼地图的非度量连续性上

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摘要

We discuss the construction of non-metric continua that support Whitney maps and their properties. We indicate a technique for producing non-metric indecomposable continua that support Whitney maps from certain compact totally disconnected spaces each of which allows a self-homeomorphism all of whose orbits are dense. These are non-metric examples that have the property that each proper subcontinuum is metric. Both perfectly normal and non-perfectly normal examples are constructed. We describe techniques for producing large collections of non-homeomorphic continua that support Whitney maps. An example of a continuum every non-degenerate subcontinuum of which is non-metric that supports a Whitney map is constructed; an example of a continuum that does not support a Whitney map which is the union of two subcontinua each of which supports a Whitney map is constructed.
机译：我们讨论了支持惠特尼地图及其属性的非度量连续体的构造。我们指出了一种用于产生非度量不可分解连续体的技术，该技术从某些紧凑的完全不相连的空间支持惠特尼图，每个空间都允许自同胚，其所有轨道都是密集的。这些是非度量示例，其属性是每个适当的子连续体都是度量。构造了完全正常和非完全正常的示例。我们描述了用于生成大量支持Whitney映射的非同胚连续性集合的技术。构造一个连续体的示例，该连续体的每个非退化子连续体都是非度量的，支持惠特尼图。一个不支持惠特尼图的连续体的示例，惠特尼图是两个子连续体的联合，每个子连续体都支持惠特尼图。

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