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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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Open maps of chainable continua
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by Ira Rosenholtz PDF
Proc. Amer. Math. Soc. 42 (1974), 258-264 Request permission

Abstract:

It is apparently “well known” that the image of the closed unit interval under an open map is homeomorphic to the closed unit interval (see [13], [11], and [15]). In this paper, we generalize this result to chainable continua. In particular, the fact that the open continuous image of a chainable continuum is also chainable is proved, answering a question of A. Lelek (see [10]). This fact, as well as its proof, implies that the open continuous image of the pseudo-arc is also a pseudo-arc. An additional corollary (of the proof) is that a local homeomorphism of a chainable continuum is actually a homeomorphism. The proofs are all very elementary.
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 42 (1974), 258-264
  • MSC: Primary 54F20; Secondary 54C10
  • DOI: https://doi.org/10.1090/S0002-9939-1974-0331346-8
  • MathSciNet review: 0331346