Whitney maps-a non-metric case

Janusz Charatonik; Włodzimierz Charatonik

Colloquium Mathematicae (2000)

  • Volume: 83, Issue: 2, page 305-307
  • ISSN: 0010-1354

Abstract

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It is shown that there is no Whitney map on the hyperspace 2 X for non-metrizable Hausdorff compact spaces X. Examples are presented of non-metrizable continua X which admit and ones which do not admit a Whitney map for C(X).

How to cite

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Charatonik, Janusz, and Charatonik, Włodzimierz. "Whitney maps-a non-metric case." Colloquium Mathematicae 83.2 (2000): 305-307. <http://eudml.org/doc/210789>.

@article{Charatonik2000,
abstract = {It is shown that there is no Whitney map on the hyperspace $2^X$ for non-metrizable Hausdorff compact spaces X. Examples are presented of non-metrizable continua X which admit and ones which do not admit a Whitney map for C(X).},
author = {Charatonik, Janusz, Charatonik, Włodzimierz},
journal = {Colloquium Mathematicae},
keywords = {Whitney map; hyperspace; metrizable; continuum; non-metrizable continua},
language = {eng},
number = {2},
pages = {305-307},
title = {Whitney maps-a non-metric case},
url = {http://eudml.org/doc/210789},
volume = {83},
year = {2000},
}

TY - JOUR
AU - Charatonik, Janusz
AU - Charatonik, Włodzimierz
TI - Whitney maps-a non-metric case
JO - Colloquium Mathematicae
PY - 2000
VL - 83
IS - 2
SP - 305
EP - 307
AB - It is shown that there is no Whitney map on the hyperspace $2^X$ for non-metrizable Hausdorff compact spaces X. Examples are presented of non-metrizable continua X which admit and ones which do not admit a Whitney map for C(X).
LA - eng
KW - Whitney map; hyperspace; metrizable; continuum; non-metrizable continua
UR - http://eudml.org/doc/210789
ER -

References

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  1. [1] R. Engelking, General Topology, Heldermann, Berlin, 1989. 
  2. [2] A. Gutek, A generalization of solenoids, in: Topology (Budapest, 1978), Colloq. Math. Soc. János Bolyai 23, North-Holland, Amsterdam, 1980, 547-554. 
  3. [3] A. Gutek and C. L. Hagopian, A nonmetric indecomposable homogeneous continuum every proper subcontinuum of which is an arc, Proc. Amer. Math. Soc. 86 (1982), 169-172. Zbl0489.54031
  4. [4] A. Illanes and S. B. Nadler, Jr., Hyperspaces, Dekker, New York, 1999. 
  5. [5] S. B. Nadler, Jr., Hyperspaces of Sets, Dekker, New York, 1978. 

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