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On the space of functions without discontinuities of the second kind


Author: L. Š. Grinblat
Journal: Proc. Amer. Math. Soc. 60 (1976), 373-375
MSC: Primary 54E50; Secondary 60B10
MathSciNet review: 0423313
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Abstract: In this note we prove a general theorem which implies the famous proposition that the space of functions without discontinuities of the second kind, equipped with the Skorohod metric, is homeomorphic to a complete metric space.


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

  • [1] Gordon Thomas Whyburn, Analytic Topology, American Mathematical Society Colloquium Publications, v. 28, American Mathematical Society, New York, 1942. MR 0007095
  • [2] Waclaw Sierpinski, General topology, Mathematical Expositions, No. 7, University of Toronto Press, Toronto, 1952. Translated by C. Cecilia Krieger. MR 0050870
  • [3] Patrick Billingsley, Convergence of probability measures, John Wiley & Sons, Inc., New York-London-Sydney, 1968. MR 0233396
  • [4] Ĭ. Ī. Gīhman and A. V. Skorohod, The theory of stochastic processes. I, Springer-Verlag, New York-Heidelberg, 1974. Translated from the Russian by S. Kotz; Die Grundlehren der mathematischen Wissenschaften, Band 210. MR 0346882

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DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0423313-2
Article copyright: © Copyright 1976 American Mathematical Society