| Title:
|
On generalized homogeneity of locally connected plane continua (English) |
| Author:
|
Charatonik, Janusz J. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
32 |
| Issue:
|
4 |
| Year:
|
1991 |
| Pages:
|
769-774 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The well-known result of S. Mazurkiewicz that the simple closed curve is the only nondegenerate locally connected plane homogeneous continuum is extended to generalized homogeneity with respect to some other classes of mappings. Several open problems in the area are posed. (English) |
| Keyword:
|
confluent |
| Keyword:
|
continuum |
| Keyword:
|
dendrite |
| Keyword:
|
homogeneous |
| Keyword:
|
light |
| Keyword:
|
local homeomorphism |
| Keyword:
|
locally connected |
| Keyword:
|
monotone |
| Keyword:
|
open |
| Keyword:
|
plane |
| Keyword:
|
simple closed curve |
| Keyword:
|
universal plane curve |
| MSC:
|
54C10 |
| MSC:
|
54F15 |
| MSC:
|
54F50 |
| idZBL:
|
Zbl 0786.54035 |
| idMR:
|
MR1159824 |
| . |
| Date available:
|
2009-01-08T17:49:14Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118457 |
| . |
| Reference:
|
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| Reference:
|
[2] Anderson R.D.: One-dimensional continuous curves and a homogeneity theorem.Ann. of Math. (2) 68 (1958), 1-16. Zbl 0083.17608, MR 0096181 |
| Reference:
|
[3] Bing R.H.: A simple closed curve is the only homogeneous bounded plane continuum that contains an arc.Canad. J. Math. 12 (1960), 209-230. Zbl 0091.36204, MR 0111001 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[8] Charatonik J.J.: Monotone mappings of universal dendrites.Topology Appl. 38 (1991), 163-167. Zbl 0726.54012, MR 1094549 |
| Reference:
|
[9] Charatonik J.J., Omiljanowski K.: On light open mappings.Proceedings International Topological Conference, Baku (USSR), l989, 211-219. Zbl 0817.54010, MR 1347226 |
| Reference:
|
[10] Kato H.: Generalized homogeneity of continua and a question of J.J. Charatonik.Houston J. Math. 13 (1987), 51-63. Zbl 0635.54017, MR 0884233 |
| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
|
[14] Prajs J.R.: On open homogeneity of closed balls in the Euclidean spaces.preprint. |
| Reference:
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| Reference:
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| Reference:
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| Reference:
|
[18] Wilson D.C.: Open mappings of the universal curve onto continuous curves.Trans. Amer. Math. Soc. 168 (1972), 497-515. Zbl 0239.54007, MR 0298630 |
| . |
