Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Baire spaces and Vietoris hyperspaces
HTML articles powered by AMS MathViewer

by Jiling Cao, Salvador García-Ferreira and Valentin Gutev PDF
Proc. Amer. Math. Soc. 135 (2007), 299-303 Request permission

Erratum: Proc. Amer. Math. Soc. 136 (2008), 3729-3731.


We prove that if the Vietoris hyperspace $CL(X)$ of all nonempty closed subsets of a space $X$ is Baire, then all finite powers of $X$ must be Baire spaces. In particular, there exists a metrizable Baire space $X$ whose Vietoris hyperspace $CL(X)$ is not Baire. This settles an open problem of R. A. McCoy stated in 1975.
Similar Articles
Additional Information
  • Jiling Cao
  • Affiliation: Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland 1, New Zealand
  • Address at time of publication: School of Mathematical Sciences, Auckland University of Technology, Private Bag 92006, Auckland 1020, New Zealand
  • Email:
  • Salvador García-Ferreira
  • Affiliation: Instituto de Matematicas (UNAM), Apartado Postal 61-3, Xangari 58089, Morelia, Michoacan, Mexico
  • Email:
  • Valentin Gutev
  • Affiliation: School of Mathematical Sciences, Faculty of Science, University of KwaZulu-Natal, King George V Avenue, Durban 4041, South Africa
  • Email:
  • Received by editor(s): September 2, 2004
  • Published electronically: August 16, 2006
  • Additional Notes: The first author’s research was supported by the Foundation for Research, Science and Technology of New Zealand under project number UOAX0240.
    The third author’s research was partially supported by the National Research Foundation of South Africa under grant number 2053735.
  • Communicated by: Jonathan M. Borwein
  • © Copyright 2006 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 135 (2007), 299-303
  • MSC (2000): Primary 54E52; Secondary 26A21, 46A30, 54B10, 54B20
  • DOI:
  • MathSciNet review: 2280197