| Title:
|
A continuum $X$ such that $C(X)$ is not continuously homogeneous (English) |
| Author:
|
Illanes, Alejandro |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
57 |
| Issue:
|
1 |
| Year:
|
2016 |
| Pages:
|
97-101 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
continuum |
| Keyword:
|
continuously homogeneous |
| Keyword:
|
hyperspace |
| MSC:
|
54B20 |
| MSC:
|
54F15 |
| idZBL:
|
Zbl 06562200 |
| idMR:
|
MR3478343 |
| DOI:
|
10.14712/1213-7243.2015.146 |
| . |
| Date available:
|
2016-04-12T05:07:26Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144919 |
| . |
| Reference:
|
[1] Charatonik J.J., Charatonik W.J.: A degree of nonlocal connectedness.Rocky Mountain J. Math. 31 (2001), 1205–1236. MR 1895293, 10.1216/rmjm/1021249438 |
| Reference:
|
[2] Charatonik W.J., Garncarek Z.: Some remarks on continuously homogeneous continua.Bull. Polish. Acad. Sci. Math. 32 (1984), 339–342. MR 0785993 |
| Reference:
|
[3] Engelking R., Lelek A.: Cartesian products and continuous images.Colloq. Math. 8 (1961), 27–29. MR 0131263 |
| Reference:
|
[4] Goodykoontz J.T., Jr.: More on connectedness im kleinen and local connectedness in $C(X)$.Proc. Amer. Math. Soc. 65 (1977), 357–364. MR 0451188 |
| Reference:
|
[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. MR 1670250 |
| . |
