Abstract
A continuous analogue to the partition lattices is presented. This is the metric completion of the direct limit of a system of embeddings of the finite partition lattices. The construction is analogous to von Neumann's construction of a continuous geometry over a field F from the finite-dimensional projective geometries over F.
Keywords: continuous geometry, geometric lattice, matroid, measure-preserving permutation
Full text
PDF
Selected References
These references are in PubMed. This may not be the complete list of references from this article.
- Neumann J. V. Continuous Geometry. Proc Natl Acad Sci U S A. 1936 Feb;22(2):92–100. doi: 10.1073/pnas.22.2.92. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Neumann J. V. Continuous Rings and Their Arithmetics. Proc Natl Acad Sci U S A. 1937 Jun;23(6):341–349. doi: 10.1073/pnas.23.6.341. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Neumann J. V. Examples of Continuous Geometries. Proc Natl Acad Sci U S A. 1936 Feb;22(2):101–108. doi: 10.1073/pnas.22.2.101. [DOI] [PMC free article] [PubMed] [Google Scholar]