Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Continuously homogeneous continua and their arc components

Author: Janusz R. Prajs
Journal: Proc. Amer. Math. Soc. 101 (1987), 533-540
MSC: Primary 54F20; Secondary 54F65
MathSciNet review: 908664
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ X$ be a continuously homogeneous Hausdorff continuum. We prove that if there is a sequence $ {A_1},{A_2}, \ldots $ of its arc components with $ X = {\text{c1}}{A_1} \cup {\text{c1}}{A_2} \cup \cdots $, and there is an arc component of $ X$ with nonempty interior, then $ X$ is arcwise connected. As consequences and applications we get: (1) if $ X$ is the countable union of arcwise connected continua, then $ X$ is arcwise connected; (2) if $ X$ is nondegenerate and metric, the number of its arc components is countable and it contains no simple triod, then it is either an arc or a simple closed curve; and, in particular, (3) an arc is the only nondegenerate continuously homogeneous arc-like metric continuum with countably many arc components.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54F20, 54F65

Retrieve articles in all journals with MSC: 54F20, 54F65

Additional Information

Keywords: Continuous homogeneity, covering sequence, Hausdorff continuum, $ \mathcal{K}$-component, simple triod
Article copyright: © Copyright 1987 American Mathematical Society

American Mathematical Society