Uniform order-convergence for complete lattices
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- by Gabriele H. Greco
- Proc. Amer. Math. Soc. 90 (1984), 657-658
- DOI: https://doi.org/10.1090/S0002-9939-1984-0733422-0
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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
- Garrett Birkhoff, Lattice theory, 3rd ed., American Mathematical Society Colloquium Publications, Vol. XXV, American Mathematical Society, Providence, R.I., 1967. MR 0227053
- Orrin Frink Jr., Topology in lattices, Trans. Amer. Math. Soc. 51 (1942), 569–582. MR 6496, DOI 10.1090/S0002-9947-1942-0006496-X
- George N. Raney, A subdirect-union representation for completely distributive complete lattices, Proc. Amer. Math. Soc. 4 (1953), 518–522. MR 58568, DOI 10.1090/S0002-9939-1953-0058568-4
Bibliographic Information
- © Copyright 1984 American Mathematical Society
- 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