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Lattice Uniformities on Effect Algebras

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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.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università della Basilicata Contrada Macchia Romana, Potenza, Italy

    Anna Avallone & Paolo Vitolo

  2. Dipartimento di Matematica, Università della Basilicata Contrada Macchia Romana, 85100, Potenza, Italy

    Anna Avallone

Authors
  1. Anna Avallone
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  2. Paolo Vitolo
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Correspondence to Anna Avallone.

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Avallone, A., Vitolo, P. Lattice Uniformities on Effect Algebras. Int J Theor Phys 44, 793–806 (2005). https://doi.org/10.1007/s10773-005-7057-8

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  • DOI: https://doi.org/10.1007/s10773-005-7057-8

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