Lattice uniformities on pseudo-D-lattices

Year, pages: 2012, 1019 - 1044

Let $L$ be a pseudo-D-lattice. We prove that the lattice uniformities on $L$ which make uniformly continuous the operations of $L$ are uniquely determined by their system of neighbourhoods of $0$ and form a distributive lattice. Moreover we prove that every such uniformity is generated by a family of weakly subadditive $[0,+∞]$-valued functions on $L$.

Avallone, A., Vitolo, P. 2012. Lattice uniformities on pseudo-D-lattices. In Mathematica Slovaca, vol. 62, no.6, pp. 1019-1044. 0139-9918. DOI: https://doi.org/10.2478/s12175-012-0062-5

Avallone, A., Vitolo, P. (2012). Lattice uniformities on pseudo-D-lattices. Mathematica Slovaca, 62(6), 1019-1044. 0139-9918. DOI: https://doi.org/10.2478/s12175-012-0062-5