Communications in Mathematical Physics

, Volume 259, Issue 2, pp 363–366

Orthomodular Lattices Generated by Graphs of Functions

Article

DOI: 10.1007/s00220-005-1362-1

Cite this article as:
Cegła, W. & Florek, J. Commun. Math. Phys. (2005) 259: 363. doi:10.1007/s00220-005-1362-1

Abstract

In a subset https://static-content.springer.com/image/art%3A10.1007%2Fs00220-005-1362-1/MediaObjects/s00220-005-1362-1flb1.gif where ℝ is the real line and https://static-content.springer.com/image/art%3A10.1007%2Fs00220-005-1362-1/MediaObjects/s00220-005-1362-1flb2.gif is an arbitrary topological space, an orthogonality relation is constructed from a family of graphs of continuous functions from connected subsets of ℝ to https://static-content.springer.com/image/art%3A10.1007%2Fs00220-005-1362-1/MediaObjects/s00220-005-1362-1flb2.gif. It is shown that under two conditions on this family a complete lattice of double orthoclosed sets is orthomodular.

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Institute of Theoretical PhysicsUniversity of WrocławWrocławPoland
  2. 2.Institute of MathematicsUniversity of EconomicsWrocławPoland