A continuum X such that C ( X ) is not continuously homogeneous

Alejandro Illanes

Commentationes Mathematicae Universitatis Carolinae (2016)

  • Volume: 57, Issue: 1, page 97-101
  • ISSN: 0010-2628

Abstract

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A metric continuum X is said to be continuously homogeneous provided that for every two points p , q ∈ X there exists a continuous surjective function f : X → X such that f ( p ) = q . Answering a question by W.J. Charatonik and Z. Garncarek, in this paper we show a continuum X such that the hyperspace of subcontinua of X , C ( X ) , is not continuously homogeneous.

How to cite

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Illanes, Alejandro. "A continuum $X$ such that $C(X)$ is not continuously homogeneous." Commentationes Mathematicae Universitatis Carolinae 57.1 (2016): 97-101. <http://eudml.org/doc/276799>.

@article{Illanes2016,
abstract = {A metric continuum $X$ is said to be continuously homogeneous provided that for every two points $p,q\in X$ there exists a continuous surjective function $f:X\rightarrow X$ such that $f(p)=q$. Answering a question by W.J. Charatonik and Z. Garncarek, in this paper we show a continuum $X$ such that the hyperspace of subcontinua of $X$, $C(X)$, is not continuously homogeneous.},
author = {Illanes, Alejandro},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {continuum; continuously homogeneous; hyperspace},
language = {eng},
number = {1},
pages = {97-101},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A continuum $X$ such that $C(X)$ is not continuously homogeneous},
url = {http://eudml.org/doc/276799},
volume = {57},
year = {2016},
}

TY - JOUR
AU - Illanes, Alejandro
TI - A continuum $X$ such that $C(X)$ is not continuously homogeneous
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2016
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 57
IS - 1
SP - 97
EP - 101
AB - A metric continuum $X$ is said to be continuously homogeneous provided that for every two points $p,q\in X$ there exists a continuous surjective function $f:X\rightarrow X$ such that $f(p)=q$. Answering a question by W.J. Charatonik and Z. Garncarek, in this paper we show a continuum $X$ such that the hyperspace of subcontinua of $X$, $C(X)$, is not continuously homogeneous.
LA - eng
KW - continuum; continuously homogeneous; hyperspace
UR - http://eudml.org/doc/276799
ER -

References

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  1. Charatonik J.J., Charatonik W.J., 10.1216/rmjm/1021249438, Rocky Mountain J. Math. 31 (2001), 1205–1236. MR1895293DOI10.1216/rmjm/1021249438
  2. Charatonik W.J., Garncarek Z., Some remarks on continuously homogeneous continua, Bull. Polish. Acad. Sci. Math. 32 (1984), 339–342. MR0785993
  3. Engelking R., Lelek A., Cartesian products and continuous images, Colloq. Math. 8 (1961), 27–29. MR0131263
  4. Goodykoontz J.T., Jr., More on connectedness im kleinen and local connectedness in C ( X ) , Proc. Amer. Math. Soc. 65 (1977), 357–364. MR0451188
  5. Illanes A., Nadler S.B., Jr., Hyperspaces: Fundamentals and Recent Advances, Monographs and Textbooks in Pure and Applied Mathematics, 216, Marcel Dekker, Inc., New York and Basel, 1999. MR1670250

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