Exactly two-to-one maps from continua onto arc-continua

Wojciech Dębski; J. Heath; J. Mioduszewski

Fundamenta Mathematicae (1996)

  • Volume: 150, Issue: 2, page 113-126
  • ISSN: 0016-2736

Abstract

top
Continuing studies on 2-to-1 maps onto indecomposable continua having only arcs as proper non-degenerate subcontinua - called here arc-continua - we drop the hypothesis of tree-likeness, and we get some conditions on the arc-continuum image that force any 2-to-1 map to be a local homeomorphism. We show that any 2-to-1 map from a continuum onto a local Cantor bundle Y is either a local homeomorphism or a retraction if Y is orientable, and that it is a local homeomorphism if Y is not orientable.

How to cite

top

Dębski, Wojciech, Heath, J., and Mioduszewski, J.. "Exactly two-to-one maps from continua onto arc-continua." Fundamenta Mathematicae 150.2 (1996): 113-126. <http://eudml.org/doc/212165>.

@article{Dębski1996,
abstract = {Continuing studies on 2-to-1 maps onto indecomposable continua having only arcs as proper non-degenerate subcontinua - called here arc-continua - we drop the hypothesis of tree-likeness, and we get some conditions on the arc-continuum image that force any 2-to-1 map to be a local homeomorphism. We show that any 2-to-1 map from a continuum onto a local Cantor bundle Y is either a local homeomorphism or a retraction if Y is orientable, and that it is a local homeomorphism if Y is not orientable.},
author = {Dębski, Wojciech, Heath, J., Mioduszewski, J.},
journal = {Fundamenta Mathematicae},
keywords = {local bundle; arc-continuum; local homeomorphism},
language = {eng},
number = {2},
pages = {113-126},
title = {Exactly two-to-one maps from continua onto arc-continua},
url = {http://eudml.org/doc/212165},
volume = {150},
year = {1996},
}

TY - JOUR
AU - Dębski, Wojciech
AU - Heath, J.
AU - Mioduszewski, J.
TI - Exactly two-to-one maps from continua onto arc-continua
JO - Fundamenta Mathematicae
PY - 1996
VL - 150
IS - 2
SP - 113
EP - 126
AB - Continuing studies on 2-to-1 maps onto indecomposable continua having only arcs as proper non-degenerate subcontinua - called here arc-continua - we drop the hypothesis of tree-likeness, and we get some conditions on the arc-continuum image that force any 2-to-1 map to be a local homeomorphism. We show that any 2-to-1 map from a continuum onto a local Cantor bundle Y is either a local homeomorphism or a retraction if Y is orientable, and that it is a local homeomorphism if Y is not orientable.
LA - eng
KW - local bundle; arc-continuum; local homeomorphism
UR - http://eudml.org/doc/212165
ER -

References

top
  1. [1] J. M. Aarts, The structure of orbits in dynamical systems, Fund. Math. 129 (1988), 39-58. Zbl0664.54026
  2. [2] J. M. Aarts and M. Martens, Flows on one-dimensional spaces, Fund. Math. 131 (1988), 53-67. 
  3. [3] J. M. Aarts and L. G. Oversteegen, Flowbox manifolds, Trans. Amer. Math. Soc. 327 (1991), 449-463. Zbl0768.54027
  4. [4] W. Dębski, Two-to-one maps on solenoids and Knaster continua, Fund. Math. 141 (1992), 277-285. Zbl0822.54028
  5. [5] W. Dębski, J. Heath and J. Mioduszewski, Exactly two-to-one maps from continua onto some tree-like continua, Fund. Math., 269-276. Zbl0807.54015
  6. [6] W. H. Gottschalk, On k-to-1 transformations, Bull. Amer. Math. Soc. 53 (1947), 168-169. Zbl0040.25402
  7. [7] J. Grispolakis and E. D. Tymchatyn, Continua which are images of weakly confluent mappings only, (I), Houston J. Math. 5 (1979), 483-501. Zbl0412.54039
  8. [8] O. G. Harrold, Exactly (k,1) transformations on connected linear graphs, Amer. J. Math. 62 (1940), 823-834. Zbl0024.19101
  9. [9] J. Heath, 2-to-1 maps with hereditarily indecomposable images, Proc. Amer. Math. Soc. 113 (1991), 839-846. Zbl0738.54012
  10. [10] J. Heath, There is no exactly k-to-1 function from any continuum onto [0,1], or any dendrite, with only finitely many discontinuities, Trans. Amer. Math. Soc. 306 (1988), 293-305. Zbl0649.54006
  11. [11] J. Hocking and G. Young, Topology, Addison-Wesley, 1961. 
  12. [12] H. B. Keynes and M. Sears, Modeling expansion in real flows, Pacific J. Math. 85 (1979), 111-124. 
  13. [13] J. Mioduszewski, On two-to-one continuous functions, Dissertationes Math. (Rozprawy Mat.) 24 (1961). Zbl0104.17304
  14. [14] S. B. Nadler, Jr. and L. E. Ward, Jr., Concerning exactly (n,1) images of continua, Proc. Amer. Math. Soc. 87 (1983), 351-354. Zbl0503.54018

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.