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Transfinite sequences of continuous and Baire class 1 functions

Author(s): Márton Elekes; Kenneth Kunen
Journal: Proc. Amer. Math. Soc. 131 (2003), 2453-2457.
MSC (2000): Primary 26A21; Secondary 03E17, 54C30
Posted: November 13, 2002
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Abstract: The set of continuous or Baire class 1 functions defined on a metric space 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 .

References:

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

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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: 10.1090/S0002-9939-02-06775-8
PII: S 0002-9939(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.
Posted: November 13, 2002
Additional Notes: The second author was partially supported by NSF Grant DMS-0097881
Communicated by: Alan Dow
Copyright of article: Copyright 2002, American Mathematical Society


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