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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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Directed inverse limits of spatial locales
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by Wei He and Till Plewe PDF
Proc. Amer. Math. Soc. 130 (2002), 2811-2814 Request permission

Abstract:

In this note we consider spatiality of directed inverse limits of spatial locales. We give an example which shows that directed inverse limits of compact spatial locales are not necessarily spatial. This answers a question posed by John Isbell. We also give a condition which, if satisfied by the maps of a directed inverse system, implies that taking limits preserves local compactness and hence produces spatial locales.
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Additional Information
  • Wei He
  • Affiliation: Department of Mathematics, Shaan Xi Normal University, Xi’an 710062, People’s Republic of China
  • Address at time of publication: Department of Mathematics, Nanjing Normal University, Nanjing 210097, People’s Republic of China
  • Email: weihe@snnu.edu.cn, weihe@njnu.edu.cn
  • Till Plewe
  • Affiliation: Department of Science and Engineering, Ritsumeikan University, Noji Higashi 1-1-1, Kusatsu-shi, Shiga 525, Japan
  • Email: till@theory.cs.ritsumei.ac.jp
  • Received by editor(s): May 17, 1998
  • Received by editor(s) in revised form: October 30, 2000
  • Published electronically: May 8, 2002
  • Additional Notes: The first author was supported by a grant of the NSF of China
  • Communicated by: Alan Dow
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 130 (2002), 2811-2814
  • MSC (2000): Primary 18B30, 54B30, 54D30, 54D45
  • DOI: https://doi.org/10.1090/S0002-9939-02-06196-8
  • MathSciNet review: 1908261