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On Lattices of Uniformities

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Abstract

We study lattice theoretical properties of lattices of uniformities such as modularity, distributive laws and the existence of (relative) complements. For this the concepts of permutable uniformities (see Definition 3.1) and independent uniformities (see Definition 4.1) are important. Moreover, we show that e.g. the lattice of all lattice uniformities on a lattice L is a closed sublattice of the lattice of all uniformities on L.

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  1. Dipartimento di Matematica e Informatica, Università di Udine, Via delle Scienze 206, 33100, Udine, Italy

    Hans Weber

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  1. Hans Weber
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Weber, H. On Lattices of Uniformities. Order 24, 249–276 (2007). https://doi.org/10.1007/s11083-007-9071-3

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