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Lattice Uniformities on Effect Algebras |
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| Authors: | Anna?Avallone author-information" > author-information__contact u-icon-before" > mailto:avallone@unibas.it" title=" avallone@unibas.it" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author,Paolo?Vitolo |
| Affiliation: | (1) Dipartimento di Matematica, Università della Basilicata Contrada Macchia Romana, Potenza, Italy;(2) Dipartimento di Matematica, Università della Basilicata Contrada Macchia Romana, 85100 Potenza, Italy |
| Abstract: | Let L be a lattice ordered effect algebra. We prove that the lattice uniformities on L which make uniformly continuous the operations − and + of L are uniquely determined by their system of neighborhoods 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. |
| Keywords: | effect algebras lattice uniformities submeasures |
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