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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
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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?)

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Additional Information

Márton Elekes
Affiliation: Department of Analysis, Eötvös Loránd University, Budapest, Pázmány Péter sétány 1/c, 1117, Hungary
Email: emarci@cs.elte.hu

Kenneth Kunen
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Email: kunen@math.wisc.edu

DOI: https://doi.org/10.1090/S0002-9939-02-06775-8
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