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)



Transfinite sequences of continuous and Baire class 1 functions

Authors: Márton Elekes and Kenneth Kunen
Journal: Proc. Amer. Math. Soc. 131 (2003), 2453-2457
MSC (2000): Primary 26A21; Secondary 03E17, 54C30
Published electronically: November 13, 2002
MathSciNet review: 1974643
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The set of continuous or Baire class 1 functions defined on a metric space $X$ is endowed with the natural pointwise partial order. We investigate how the possible lengths of well-ordered monotone sequences (with respect to this order) depend on the space $X$.

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

  • 1. J. Brendle, S. Fuchino, and L. Soukup, Coloring ordinals by reals, to appear.
  • 2. E. K. van Douwen, The integers and topology, in Handbook of Set-Theoretic Topology, North-Holland, Amsterdam, 1984, pp. 111-167.MR 87f:54008
  • 3. M. Elekes, Linearly ordered families of Baire 1 functions, Real Analysis Exchange, 27 (2001/02), 49-63.
  • 4. I. Juhász and K. Kunen, The power set of $\omega$, Fundamenta Mathematicae, Vol 170 (2001), 257-265.
  • 5. P. Komjáth, Ordered families of Baire-2-functions, Real Analysis Exchange, Vol 15 (1989-90), 442-444. MR 91d:26007
  • 6. K. Kunen, Inaccessibility Properties of Cardinals, Doctoral Dissertation, Stanford, 1968.
  • 7. K. Kuratowski, Topology, Vol. 1, Academic Press, 1966. MR 36:840

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 26A21, 03E17, 54C30

Retrieve articles in all journals with MSC (2000): 26A21, 03E17, 54C30

Additional Information

Márton Elekes
Affiliation: Department of Analysis, Eötvös Loránd University, Budapest, Pázmány Péter sétány 1/c, 1117, Hungary

Kenneth Kunen
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706

Keywords: Baire class 1, separable metric space, transfinite sequence of functions
Received by editor(s): December 11, 2001
Received by editor(s) in revised form: March 13, 2002
Published electronically: November 13, 2002
Additional Notes: The second author was partially supported by NSF Grant DMS-0097881
Communicated by: Alan Dow
Article copyright: © Copyright 2002 American Mathematical Society

American Mathematical Society