THE PSEUDO-ARC

Wayne Lewis
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引用次数: 68

Abstract

The pseudo-arc is the simplest nondegenerate hereditarily indecomposable continuum. It is, however, also the most important, being homogeneous, having several characterizations, and having a variety of useful mapping properties. The pseudo-arc has appeared in many areas of continuum theory, as well as in several topics in geometric topology, and is beginning to make its appearance in dynamical systems. In this monograph, we give a survey of basic results and examples involving the pseudo-arc. A more complete treatment will be given in a book [133] dedicated to this topic, currently under preparation by this author. We omit formal proofs from this presentation, but do try to give indications of some basic arguments and construction techniques. Our presentation covers the following major topics. 1. Construction 2. Homogeneity 3. Characterizat ions 4. Mapping properties 5. Hyperspaces 6. Homeomorphism groups 7. Continuous decompositions 8. Dynamics
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的PSEUDO-ARC
伪弧是最简单的非简并遗传不可分解连续体。然而,它也是最重要的,它是同构的,具有多个特征,并具有各种有用的映射属性。伪弧已经出现在连续统理论的许多领域,以及几何拓扑学的几个主题中,并开始在动力系统中出现。在这篇专著中,我们给出了关于伪弧的基本结果和例子的综述。一个更完整的处理将在一本书[133]中给出,专门讨论这个话题,目前作者正在准备中。我们在本演示中省略了形式证明,但确实尝试给出一些基本论证和构造技术的指示。我们的演讲涵盖了以下主要主题。1. 建设2。同质性3。4.特征分析映射属性货币6。同胚群连续分解8。动力学
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