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A note on $ C\sb{c}(X)$


Authors: G. D. Richardson and D. C. Kent
Journal: Proc. Amer. Math. Soc. 49 (1975), 441-445
MSC: Primary 54C35; Secondary 54A20
DOI: https://doi.org/10.1090/S0002-9939-1975-0370483-X
MathSciNet review: 0370483
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Abstract: When $ X$ is a locally convex topological linear space, the function algebra $ {C_c}(X)$ (with continuous convergence) can have a closure operator which has infinitely many distinct iterations. The reverse situation is also possible: $ X$ can be a locally compact $ c$-embedded convergence space whose closure operator has infinitely many distinct iterations, whereas $ {C_c}(X)$ is a topological space.


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

  • [1] R. F. Arens, A topology for spaces of transformations, Ann. of Math. (2) 47 (1946), 480-495. MR 8, 165. MR 0017525 (8:165e)
  • [2] E. Binz, Bemerkungen zu limitierten Funktionenalgebren, Math. Ann. 175 (1968), 169-184. MR 36 #4513. MR 0221461 (36:4513)
  • [3] E. Binz, Zu den Beziehungen zwischen $ c$-einbettbaren Limesräumen und ihren limitierten Funktionenalgebren, Math. Ann. 181 (1969), 45-52. MR 39 #7552. MR 0246248 (39:7552)
  • [4] C. H. Cook and H. R. Fischer, On equicontinuity and continuous convergence, Math. Ann. 159 (1965), 94-104. MR 31 #3995. MR 0179752 (31:3995)
  • [5] D. C. Kent and G. D. Richardson, The decomposition series of a convergence space, Czechoslovak Math. J. 23 (1973), 437-446. MR 0322773 (48:1134)
  • [6] M. Schroder, G. Richardson, K. McKennon and D. Kent, Continuous convergence in $ C(X)$, Pacific J. Math. (to appear). MR 0370482 (51:6709)
  • [7] C. Wingren, Locally convex limit spaces, Acta Acad. Aboensis Ser. B 33 (1973), 1-14. MR 0324360 (48:2712)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0370483-X
Keywords: Convergence space, continuous convergence, $ c$-embedded space, highly nontopological space
Article copyright: © Copyright 1975 American Mathematical Society

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