Pacific Journal of Mathematics

On local isometries of finitely compact metric spaces.

Aleksander Całka

Article information

Source
Pacific J. Math., Volume 103, Number 2 (1982), 337-345.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102723967

Mathematical Reviews number (MathSciNet)
MR705234

Zentralblatt MATH identifier
0507.54025

Subjects
Primary: 54E40: Special maps on metric spaces
Secondary: 54E45: Compact (locally compact) metric spaces

Citation

Całka, Aleksander. On local isometries of finitely compact metric spaces. Pacific J. Math. 103 (1982), no. 2, 337--345. https://projecteuclid.org/euclid.pjm/1102723967


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References

  • [1] L. E. Blumenthal, Theory and applications of distance geometry, Oxford, Clarendon Press, 1953.
  • [2] H. Busemann, The Geometry of Geodesies, Academic Press, New York, 1955.
  • [3] H. Busemann,Geometries in which the planes minimize area, Ann. Math. Pure Appl., 55 (1961), 171-189.
  • [4] A. Calka, Local isometries of compact metric spaces, to appear.
  • [5] W. A. Kirk, On locally isometric mappings of a G-space on itself, Proc. Amer. Math. Soc, 15 (1964), 584-586.
  • [6] W. A. Kirk, Isometries in G-spaces,Duke Math. J., 31 (1964), 539-541.
  • [7] W. A. Kirk,On conditions under which local isometries are motions, Colloq. Math., 22 (1971), 229-233.
  • [8] J. Szenthe, Uber ein Problem von H. Busemann, Publ. Math. Debrecen, 7 (1960), 408-413.
  • [9] J. Szenthe,Uber lokalisometrische Abbildungen von G-Raumen auf sich, Ann. Math. Pura Appl., 55 (1961), 37-46.
  • [10] J. Szenthe, Uber metrische R'ume, deren lokalisometrische Abbildungen Isometrien sind, Acta Math. Acad. Sci. Hungar, 13 (1962), 433-441.