Pacific Journal of Mathematics

Quasi dimension type. I. Types in the real line.

Jack Segal

Article information

Source
Pacific J. Math., Volume 20, Number 3 (1967), 501-534.

Dates
First available in Project Euclid: 13 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102992700

Mathematical Reviews number (MathSciNet)
MR0208572

Zentralblatt MATH identifier
0152.40003

Subjects
Primary: 54.70

Citation

Segal, Jack. Quasi dimension type. I. Types in the real line. Pacific J. Math. 20 (1967), no. 3, 501--534. https://projecteuclid.org/euclid.pjm/1102992700


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References

  • [1] R. H. Bing, Snake-like continua, Duke Math J., 18 (1951),653-663.
  • [2] H. H. Corson, and J. R. Isbell, Some Properties of strong uniformities, Quar. J. Math. (2) 11 (1960).
  • [3] M. Frechet, Les dimensions d'un ensemble abstrait, Math. Ann. 68 (1910),145-168.
  • [4] M. Frechet, Les Espaces Abstraits, Gauthier-Villars, Paris, 1928.
  • [5] H. Freudenthal, Entwicklungenvon Rumen und ihre Gruppen, Comp. Math. 4 (1937), 145-234.
  • [6] C. Kuratowski, Sur la puissance de ensemble desCnombres de dimension" au sens de M. Frechet, Fund. Math. 8 (1926), 201-208.
  • [7] C. Kuratowski and W. Sierpinski, Sur un probleme de M. Frechet concernant les dimensions des ensembles lineaires, Fund. Math. 8 (1926), 194-200.
  • [8] C. Kuratowski and S. M. Ulam, Sur un coefficient lie aux transformationscontinues d'ensembles, Fund. Math. 20 (1933),244-253.
  • [9] C. N. Maxwell, An order relation among topological spaces, Trans. Amer. Math. Soc. 99 (1961), 201-204.
  • [10] W. Sierpinski, Sur une propriete topologique des ensembles denombrables denses en soi, Fund. Math. 1 (1920), 11-16.
  • [11] W. Sierpinski, General Topology, University of Toronto Press, 1952.
  • [12] K. Sitnikov, Example of a two-dimensional set in three-dimensional Euclidean space allowing arbitrarily small deformations into a 1-dimensional polyhedron and a certain new characteristic of the dimension of sets in Euclidean spaces, Doklady Akad. Nauk SSSR(N.S.) 88, 21-24 (1953) (Russian).
  • [13] G. T. Whyburn, Analytic Topology, Amer. Math. Soc. Colloquium Publications, 1942.

See also

  • II : Jack Segal. Quasi dimension type. II. Types in $1$-dimensional spaces. Pacific Journal of Mathematics volume 25, issue 2, (1968), pp. 353-370.