Skip to main content Accessibility help
×
Home

Axioms for an n-metric Structure

  • Kerry E. Grant (a1)

Extract

From Euclid to Hilbert, and beyond, the primitive terms of geometry have been taken as “point,” “line,” etc., while “distance” plays a secondary role. The reversal of this situation is a modern development. Frechet [4], in 1906 first considered the properties of distance which should be formalized. The most significant contributions to the geometric properties of metric spaces have been by Menger [10] and Blumenthal [2; 3].

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Axioms for an n-metric Structure
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Axioms for an n-metric Structure
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Axioms for an n-metric Structure
      Available formats
      ×

Copyright

References

Hide All
1. Birkhoff, G., Metric foundations of geometry, Trans. Amer. Math. Soc. 55 (1944), 465.
2. Blumenthal, L. M., Distance Geometries, University of Missouri Studies 13, No. 2 (1938), 1142.
3. Blumenthal, L. M., Theory and applications of distance geometry (Clarendon Press, Oxford, 1953).
4. Fréchet, M., Sur quelques points du calculfunctionnel, Rend. Cire. Mat. Palermo 22 (1906), 174.
5. Froda, A., Espaces p-métriaueetleurtopologie, C. R. Acad. Sci. Paris Sér. A-B 247 (1958), 849–52.
6. Freese, R. W. and Andalafte, E. Z., A characterization of 2-betweenness in 2-metric spaces, Can. J. Math. 18 (1966), 963968.
7. Freese, R. W. and Andalafte, E. Z., Existence of 2-segments in 2-metric spaces, Fund. Math. 60 (1967), 201208.
8. Gähler, S., 2-Metrische Raume und IhreTopologischeStruktur, Math. Nachr. 25 (1963), 115148.
9. Grant, K. E., A 2-metric lattice structure, Doctoral Dissertation, St. Louis University, 1968.
10. Menger, K., UntersuchungeniiberAllgemeineMetrik, Math. Ann. 100 (1928), 75163.
11. Murphy, G. P., Convexity and embedding in a class of 2-metrics, Doctoral Dissertation, St. Louis University, 1966.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Axioms for an n-metric Structure

  • Kerry E. Grant (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed