×

Uniform order-convergence for complete lattices. (English) Zbl 0538.54032

Summary: A purely lattice-theoretical definition of uniform order-convergence of a net of functions with values in a complete lattice is introduced and shown that for completely distributive lattices the uniform order- convergence is induced by a uniformity.

MSC:

54H12 Topological lattices, etc. (topological aspects)
06D10 Complete distributivity
54E15 Uniform structures and generalizations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Garrett Birkhoff, Lattice theory, Third edition. American Mathematical Society Colloquium Publications, Vol. XXV, American Mathematical Society, Providence, R.I., 1967. · Zbl 0153.02501
[2] Orrin Frink Jr., Topology in lattices, Trans. Amer. Math. Soc. 51 (1942), 569 – 582. · Zbl 0061.39305
[3] George N. Raney, A subdirect-union representation for completely distributive complete lattices, Proc. Amer. Math. Soc. 4 (1953), 518 – 522. · Zbl 0053.35201
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.