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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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Arcs in hyperspaces which are not compact
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by L. E. Ward PDF
Proc. Amer. Math. Soc. 28 (1971), 254-258 Request permission

Abstract:

It has been known for many years that if $X$ is a metrizable continuum then ${2^X}$ (the space of closed subsets of $X$) and $C(X)$ (the subspace of connected members of ${2^X}$) are arcwise connected. These results are due to Borsuk and Mazurkiewicz [l] and J. L. Kelley [2], respectively. Quite recently M. M. McWaters [6] extended these theorems to the case of continua which are not necessarily metrizable, using Koch’s arc theorem for partially ordered spaces [3], [8]. In this note we prove these results for certain noncompact spaces by means of a simple generalization of Koch’s arc theorem.
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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 28 (1971), 254-258
  • MSC: Primary 54.55
  • DOI: https://doi.org/10.1090/S0002-9939-1971-0275376-0
  • MathSciNet review: 0275376