On a universal ultrametric space

Topology and its Applications

Volumn 103, Issue 3, 2000, Pages 339-345

  Lemin, Alex J ^a   Lemm, Vladimir A ^b  

^a MOSCOW STATE UNIVERSITY OF CIVIL ENGINEERING   (Russian Federation)

^b PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

Axiom of choice; Cardinal number; Isometric embedding; Metric space; Non Archimedean metric space; Non Archimedean normed field; P adic numbers; Ultrametric space

Indexed keywords

EID: 0013543248     PISSN: 0016660X     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0166-8641(99)00029-2     Document Type: Article

References (21)

1. J. de Groot, Non-Archimedean metrics in topology, Proc. Amer. Math. Soc. 7 (6) (1956) 948956.
2. R Hausdorff, Uber innere Abbildungen, Fund. Math. 23 (1934) 279-291.
3. M. Krasner, Nombres semi-réels et espaces ultramȩtriques, C. R. Acad. Sci. Paris 219 (1944) 433-435.
4. A.J. Lemin, On functor of Hausdorff exponent, in: Colloquium on Topology, Eger, August 1983, Budapest, 1983, p. 59.
5. A.J. Lemin, On isosceles metric spaces and groups, in: Cardinal Invariants and Mappings of Topological Spaces, Izhevsk, 1984, pp. 26-31 (in Russian).
6. A.J. Lemin, Proximity on isosceles spaces, Russian Math. Surv. 39 (1) (1984) 143-144.
7. A.J. Lemin, On stability of the property of a space being isosceles, Russian Math. Surv. 39 (5) (1984) 283-284.
8. A.J. Lemin, Transition functor to a function space in the uniform topology, Russian Math. Surv. 40 (6) (1985) 133-134.
9. A.J. Lemin, Isometric embedding of isosceles (non-Archimedean) spaces in Luclidean spaces, Soviet Math. Dokl. 32 (3) (1985) 740-744.
10. A.J. Lemin, Ultrametric spaces, topos theory and intuitionistic logic, in: Proc. International Conference on Topology, October 1987, Baku, 1987, p. 163.
11. A.J. Lemin, An application of the theory of isosceles (ultrametric) spaces to the Trnkova-Vinarek theorem, Comment. Math. Univ. Carolin. 29 (3) (1988) 421-434.
12. A.J. Lemin, Inverse images of metric spaces under non-expanding open mappings, Russian Math. Surv. 43 (3) (1988) 214-215.
13. A.J. Lemin, Ultrametric spaces and convex programming, in: Proc. Internat. Conf. on Topology, Varna, 1990, pp. 28-29.
14. A.J. Lemin, Ultrametric spaces and Boolean algebras, in: Proc. 5th Internat. Conf. "Topology and its Applications", Zagreb, 1990, p. 49.
15. A.J. Lemin, The Smirnov compactification functor is one-to-one over the class of complete first countable spaces, Topology Appl. 38 (1991) 201-204.
16. A.J. Lemin, V. Lemin, Cayley-MacLane type theorem for ultrametric spaces, in: Proc. VIII Prague Symposium "General Topology and its Relations to Modern Analysis and Algebra", Prague, 1996, pp. 60-61.
17. A.J. Lemin, V. Lemin, On uniform rationalization of ultrametrics, Topology Proc. 22 (1999) 275-283.
18. A.J. Lemin, Yu.M. Smirnov, Isometry groups of metric and ultrametric spaces and their subgroups, Russian Math. Surv. 41 (6) (1986) 213-214.
19. M.L. Rudin, Lectures on Set-Theoretic Topology, Providence, 1975.
20. T. Jech, Lectures in Set Theory, Lecture Notes in Math., Vol. 217, Springer, Berlin, 1971.
21. I. Vestfrid, On a universal ultrametric space, Ukrain. Math. Z. 46 (12) (1994) 1700-1706 (in Russian).