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Uniform order-convergence for complete lattices


Author: Gabriele H. Greco
Journal: Proc. Amer. Math. Soc. 90 (1984), 657-658
MSC: Primary 54H12; Secondary 06D10, 54C20
DOI: https://doi.org/10.1090/S0002-9939-1984-0733422-0
MathSciNet review: 733422
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Abstract: We introduce a purely lattice-theoretical definition of uniform order-convergence of a net of functions with values in a complete lattice. We will show that for completely distributive lattices the uniform order-convergence is induced by a uniformity.


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

  • [1] G. Birkhoff, Lattice theory, 3rd ed., Amer. Math. Soc. Colloq. Publ., vol. 25, Amer. Math. Soc., Providence, R.I., 1967. MR 0227053 (37:2638)
  • [2] O. Frink, Topology in lattices, Trans. Amer. Math. Soc. 51 (1942), 569-583. MR 0006496 (3:313b)
  • [3] G. N. Raney, A subdirect-union representation for completely distributive complete lattice, Proc. Amer. Math. Soc. 4 (1953), 518-522. MR 0058568 (15:389e)

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DOI: https://doi.org/10.1090/S0002-9939-1984-0733422-0
Article copyright: © Copyright 1984 American Mathematical Society

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