Abstract
A metric space (X, d) is called monotone if there is a linear order < on X and a constant c such that d(x, y) ⩽ c d(x, z) for all x < y < z in X. Topological properties of monotone metric spaces and their countable unions are investigated.
Similar content being viewed by others
References
Brunet, B.: On the dimension of ordered spaces. Collect. Math. 48(3), 303–314 (1997)
Čech, E.: Topological spaces. Revised edition by Zdeněk Frolík andMiroslav Katětov. Scientific editor, Vlastimil Pták. Editor of the English translation, Charles O. Junge, Publishing House of the Czechoslovak Academy of Sciences, Prague; Interscience Publishers John Wiley & Sons, London-New York-Sydney, 893 pp. (1966)
Engelking, R.: General Topology. Heldermann Verlag, Berlin (1989)
Hausdorff, F.: Erweiterung einer Homöomorphie. Fundam. Math. 16, 353–360 (1930)
Koumoullis, G.: Topological spaces containing compact perfect sets and Prohorov spaces. Topol. its Appl. 21(1), 59–71 (1985)
Lutzer, D.J.: On generalized ordered spaces. Dissertationes Math. Rozprawy Mat. 89, 32 (1971)
Nyikos, P.J.: Covering properties on σ-scattered spaces. In: Proceedings of the 1977 Topology Conference. Louisiana State Univ., Baton Rouge, La., 1977, II, vol. 2, 1977, pp. 509–542 (1978)
Author information
Authors and Affiliations
Corresponding author
Additional information
The first author was supported by Department of Education of the Czech Republic, research project BA MSM 6840770010. The second author was supported by Department of Education of the Czech Republic, research project BA MSM 210000010.
Rights and permissions
About this article
Cite this article
Nekvinda, A., Zindulka, O. Monotone Metric Spaces. Order 29, 545–558 (2012). https://doi.org/10.1007/s11083-011-9221-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11083-011-9221-5