Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

Baire sections for group homomorphisms


Authors: S. Graf and G. Mägerl
Journal: Proc. Amer. Math. Soc. 85 (1982), 615-618
MSC: Primary 54C65; Secondary 22C05, 28B20, 54C50
DOI: https://doi.org/10.1090/S0002-9939-1982-0660616-3
MathSciNet review: 660616
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The following result is proved: Let $ X$ and $ Y$ be compact topological groups and $ p$ be a continuous group homomorphism from $ Y$ onto $ X$. Then there exists a map $ q$ from $ X$ to $ Y$ such that $ p \circ q = {\text{i}}{{\text{d}}_X}$ and $ {q^{ - 1}}(B)$ is a Baire set in $ Y$ for every Baire subset $ B$ of $ X$.


References [Enhancements On Off] (What's this?)

  • [1] M. Bockstein, Un théorème de séparabilité pour les produits topologiques, Fund. Math. 35 (1948), 242-246. MR 0027503 (10:316b)
  • [2] S. Graf, A measurable selection theorem for compact-valued maps, Manuscripta Math. 27 (1979), 341-352. MR 534799 (82k:28012)
  • [3] P. J. Higgins, An introduction to topological groups, Cambridge Univ. Press, Cambridge, 1974. MR 0360908 (50:13355)
  • [4] J. Kupka, Strong liftings with application to measurable cross sections in locally compact groups (preprint), 1980. MR 693662 (84g:28006)
  • [5] K. Kuratowski and C. Ryll-Nardzewski, A general theorem on selectors, Bull. Acad. Polon. Sci. Sér. Sci. Math. 13 (1965), 397-403. MR 0188994 (32:6421)
  • [6] A. Pełczyński, Linear extensions, linear averagings, and their applications to linear topological classification of spaces of continuous functions, Dissertationes Math. (Rozprawy Mat.) 58 (1968). MR 0227751 (37:3335)
  • [7] M. A. Rieffel, On extensions of locally compact groups, Amer. J. Math. 88 (1966), 871-880. MR 0202912 (34:2771)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54C65, 22C05, 28B20, 54C50

Retrieve articles in all journals with MSC: 54C65, 22C05, 28B20, 54C50


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0660616-3
Keywords: Baire measurable selections, compact groups, Bockstein separation property
Article copyright: © Copyright 1982 American Mathematical Society

American Mathematical Society