Two-to-one maps on solenoids and Knaster continua

Wojciech Dębski

Fundamenta Mathematicae (1992)

  • Volume: 141, Issue: 3, page 277-285
  • ISSN: 0016-2736

Abstract

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It is shown that 2-to-1 maps cannot be defined on certain solenoids, in particular on the dyadic solenoid, and on Knaster continua.

How to cite

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Dębski, Wojciech. "Two-to-one maps on solenoids and Knaster continua." Fundamenta Mathematicae 141.3 (1992): 277-285. <http://eudml.org/doc/211966>.

@article{Dębski1992,
author = {Dębski, Wojciech},
journal = {Fundamenta Mathematicae},
keywords = {continuous involution; dyadic solenoid; Knaster continua},
language = {eng},
number = {3},
pages = {277-285},
title = {Two-to-one maps on solenoids and Knaster continua},
url = {http://eudml.org/doc/211966},
volume = {141},
year = {1992},
}

TY - JOUR
AU - Dębski, Wojciech
TI - Two-to-one maps on solenoids and Knaster continua
JO - Fundamenta Mathematicae
PY - 1992
VL - 141
IS - 3
SP - 277
EP - 285
LA - eng
KW - continuous involution; dyadic solenoid; Knaster continua
UR - http://eudml.org/doc/211966
ER -

References

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  1. [1] P. Civin, Two-to-one mappings of manifolds, Duke Math. J. 10 (1943), 49-57. Zbl0060.41012
  2. [2] A. V. Chernavskiĭ, The impossibility of a strictly double continuous partition of the homologous cube, Dokl. Akad. Nauk SSSR 144 (1962), 286-289 (in Russian). 
  3. [3] S. Eilenberg and N. Steenrod, Foundations of Algebraic Topology, Princeton Univ. Press, 1952. Zbl0047.41402
  4. [4] V. B. Fugate and T. B. McLean, Compact groups of homeomorphisms on tree-like continua, Trans. Amer. Math. Soc. 267 (1981), 609-620. Zbl0486.54028
  5. [5] O. G. Harrold, The non-existence of a certain type of continuous transformation, Duke Math. J. 5 (1939), 789-793. Zbl0022.41001
  6. [6] J. Heath, Tree-like continua and exactly k-to-1 functions, Proc. Amer. Math. Soc. 105 (1989), 765-772. Zbl0664.54008
  7. [7] E. Hewitt and K. Ross, Abstract Harmonic Analysis, Vol. I, Springer, 1963. Zbl0115.10603
  8. [8] J. Mioduszewski, On two-to-one continuous functions, Dissertationes Math. (Rozprawy Mat.) 24 (1961). Zbl0104.17304
  9. [9] L. Pontryagin, Topological Groups, Gordon and Breach, New York 1966. 
  10. [10] I. Rosenholtz, Open maps of chainable continua, Proc. Amer. Math. Soc. 42 (1974), 258-264. Zbl0276.54033
  11. [11] W. Scheffer, Maps between topological groups that are homotopic to homomorphisms, ibid. 33 (1972), 562-567. Zbl0236.22008

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