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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Homomorphisms of lattices of continuous functions


Authors: R. Mena and B. Roth
Journal: Proc. Amer. Math. Soc. 71 (1978), 11-12
MSC: Primary 46E15
DOI: https://doi.org/10.1090/S0002-9939-1978-0487414-7
MathSciNet review: 0487414
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Abstract: We prove that for Y a compact Hausdorff space, every lattice homomorphism from $ C(Y)$ to $ C(X)$ which takes each constant function on Y to the same function on X is linear.


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

  • [1] K. Geba and Z. Semadeni, On linear isotonical embedding of $ C({\Omega _1})$ into $ C({\Omega _2})$, Studia Math. 19 (1960), 303-320. MR 0117535 (22:8313)
  • [2] I. Kaplansky, Lattices of continuous functions, Bull. Amer. Math. Soc. 53 (1947), 617-623. MR 0020715 (8:587e)
  • [3] -, Lattices of continuous functions. II, Amer. J. Math. 70 (1948), 626-634. MR 0026240 (10:127a)

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DOI: https://doi.org/10.1090/S0002-9939-1978-0487414-7
Article copyright: © Copyright 1978 American Mathematical Society

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