Let L be a pseudo-D-lattice. It is known that a key role for the study of modular measures on L is the study of D-uniformities on L, i.e. lattice uniformities which make uniformly continuous the operations of L. We prove that D-uniformities on 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. These results allow to apply classical techniques for the study of modular measures on L.
Lattice Uniformities on Pseudo-D-Lattices
AVALLONE, Anna;VITOLO, Paolo
2012-01-01
Abstract
Let L be a pseudo-D-lattice. It is known that a key role for the study of modular measures on L is the study of D-uniformities on L, i.e. lattice uniformities which make uniformly continuous the operations of L. We prove that D-uniformities on 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. These results allow to apply classical techniques for the study of modular measures on L.File in questo prodotto:
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