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Let be a smooth dendroid in the plane . We show that each endpoint of is arcwise accessible from , and that the space of endpoints has the property of a circle. In the event that is connected, we call a Bellamy dendroid. We prove that if is 1-dimensional, then contains a Bellamy dendroid or a Cantor set of arcs. In particular, if totally disconnected and 1-dimensional, then is non-Suslinian. An example is constructed to show that this is false outside the plane.

生成讲解博客的中文版本

生成AI智能校验的中文版本