Continuous functions on countable compact ordered sets as sums of their increments
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- by Gadi Moran PDF
- Trans. Amer. Math. Soc. 256 (1979), 99-112 Request permission
Abstract:
Every continuous function from a countable compact linearly ordered set A into a Banach space V (vanishing at the least element of A ) admits a representation as a sum of a series of its increments (in the topology of uniform convergence). This series converges to no other sum under rearrangements of its terms. A uniqueness result to the problem of representation of a regulated real function on the unit interval as a sum of a continuous and a steplike function is derived.References
- Herbert B. Enderton, Elements of set theory, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1977. MR 0439636
- László Fuchs, Infinite abelian groups. Vol. I, Pure and Applied Mathematics, Vol. 36, Academic Press, New York-London, 1970. MR 0255673 A. Haar and D. König, Über einfach geordnete Mengen, J. Reine Angew. Math. 139 (1911), 16-28.
- H. Hadwiger, Über die Konvergenzarten unendlicher Reihen im Hilbertschen Raum, Math. Z. 47 (1941), 325–329 (German). MR 6373, DOI 10.1007/BF01180965
- Casper Goffman, Gadi Moran, and Daniel Waterman, The structure of regulated functions, Proc. Amer. Math. Soc. 57 (1976), no. 1, 61–65. MR 401993, DOI 10.1090/S0002-9939-1976-0401993-5
- John L. Kelley, General topology, D. Van Nostrand Co., Inc., Toronto-New York-London, 1955. MR 0070144
- K. Kuratowski, Topology. Vol. I, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe [Polish Scientific Publishers], Warsaw, 1966. New edition, revised and augmented; Translated from the French by J. Jaworowski. MR 0217751
- C. W. McArthur, On relationships amongst certain spaces of sequences in an arbitrary Banach space, Canadian J. Math. 8 (1956), 192–197. MR 78662, DOI 10.4153/CJM-1956-022-0
- Gadi Moran, Of regulated and steplike functions, Trans. Amer. Math. Soc. 231 (1977), no. 1, 249–257. MR 499028, DOI 10.1090/S0002-9947-1977-0499028-7
- Gadi Moran, On scattered compact ordered sets, Proc. Amer. Math. Soc. 75 (1979), no. 2, 355–360. MR 532165, DOI 10.1090/S0002-9939-1979-0532165-4
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 256 (1979), 99-112
- MSC: Primary 46E15; Secondary 40A30, 54C05
- DOI: https://doi.org/10.1090/S0002-9947-1979-0546909-3
- MathSciNet review: 546909