Hostname: page-component-848d4c4894-pjpqr Total loading time: 0 Render date: 2024-06-25T23:21:47.954Z Has data issue: false hasContentIssue false
  • English
  • Français

Brouwerian Geometry

Published online by Cambridge University Press:  20 November 2018

E. A. Nordhaus  and
Leo Lapidus
E. A. Nordhaus
Affiliation:
Michigan State College
Leo Lapidus
Affiliation:
Michigan State College
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

From time to time attention has been directed to the study of spaces in which the “distances” are selected from algebraic structures other than the real or complex numbers. For example, Menger (9) and Taussky (11) have considered spaces in which the distances are taken from a group. More recently, Ellis (4), Blumenthal (2), and Elliott (3), have investigated spaces in which the distances are elements of a lattice.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 6 , 1954 , pp. 217 - 229
Copyright
Copyright © Canadian Mathematical Society 1954

References

1. Birkhoff, Garrett, Lattice theory, Amer. Math. Soc. Colloquium Publications, 25 (1948), revised edition.Google Scholar
2. Blumenthal, L. M., Boolean geometry I, National Bureau of Standards Report 1482 (1952).Google Scholar
3. Elliott, J. G., Autometrization and the symmetric difference, Can. J. Math., 5 (1953), 324–331.Google Scholar
4. Ellis, D. O., Autometrized Boolean algebras I, Can. J. Math., 3 (1951), 87–93.Google Scholar
5. Ellis, D. O., Autometrized Boolean algebras II, Can. J. Math., 3 (1951), 145–147.Google Scholar
6. Kuratowski, C., Sur l'opération Ā de l'analysis situs, Fund. Math., 3 (1922), 182–199.Google Scholar
7. McKinsey, J. C. C. and Tarski, A., On closed elements in closure algebras, Annals of Math. 47 (1946), 122–162.Google Scholar
8. Menger, K., Untersuchungen über allgemeine Metrik II, Math. Annalen, 100 (1928), 75–163.Google Scholar
9. Menger, K., Beiträge zur Gruppentheorie I. Ueber einen Abstand in Gruppen, Math. Zeitschrift, 83 (1931), 396–418.Google Scholar
10. Pitcher, Everett and Smiley, M. F., Transitivities of betweenness, Trans. Amer. Math. Soc, 52 (1942), 95–114.Google Scholar
11. Taussky, O., Abstracte Körper und Metrik I, Ergebnisse eines Math. Kolloquiums, 6 (1935), 20–23.Google Scholar