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

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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

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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

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