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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Disk-like products of $\lambda$ connected continua. II
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by Charles L. Hagopian PDF
Proc. Amer. Math. Soc. 52 (1975), 479-484 Request permission

Abstract:

R. H. Bing [3] proved that every atriodic, hereditarily decomposable, hereditarily unicoherent continuum is arc-like. Using this theorem, the author [5] showed that $\lambda$ connected continua $X$ and $Y$ are arc-like when the topological product $X \times Y$ is disk-like. In this paper we consider products that have a more general mapping property. Suppose that $X$ and $Y$ are $\lambda$ connected continua and that for each $\varepsilon > 0$, there exists an $\varepsilon$-map of $X \times Y$ into the plane. Then $X$ is either arc-like or circle-like. Furthermore, if $X$ is circle-like, then $Y$ is arc-like. Hence $X \times Y$ is either disk-like or annulus-like.
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 52 (1975), 479-484
  • MSC: Primary 54F20
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0494000-9
  • MathSciNet review: 0494000