| Title:
|
Homotopy properties of curves (English) |
| Author:
|
Charatonik, Janusz J. |
| Author:
|
Illanes, Alejandro |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
39 |
| Issue:
|
3 |
| Year:
|
1998 |
| Pages:
|
573-580 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Conditions are investigated that imply noncontractibility of curves. In particular, a plane noncontractible dendroid is constructed which contains no homotopically fixed subset. A new concept of a homotopically steady subset of a space is introduced and its connections with other related concepts are studied. (English) |
| Keyword:
|
continuum |
| Keyword:
|
contractible |
| Keyword:
|
curve |
| Keyword:
|
deformation |
| Keyword:
|
dendroid |
| Keyword:
|
fixed |
| Keyword:
|
homotopy |
| Keyword:
|
steady |
| MSC:
|
54E40 |
| MSC:
|
54F15 |
| MSC:
|
54F50 |
| MSC:
|
54H99 |
| MSC:
|
55M99 |
| idZBL:
|
Zbl 0962.54027 |
| idMR:
|
MR1666818 |
| . |
| Date available:
|
2009-01-08T18:46:28Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119034 |
| . |
| Reference:
|
[1] Borsuk K., Jaworowski J.W.: On labil and stabil points.Fund. Math. 39 (1952), 159-175. MR 0056283 |
| Reference:
|
[2] Charatonik J.J.: Problems and remarks on contractibility of curves.General Topology and its Relations to Modern Analysis and Algebra IV, Proceedings of the Fourth Prague Topological Symposium 1976 Part B Contributed Papers Society of Czechoslovak Mathematicians and Physicists (1977), 72-76. Zbl 0373.54029, MR 0464197 |
| Reference:
|
[3] Charatonik J.J.: Contractibility of curves.Matematiche (Catania) 46 (1991), 559-592. Zbl 0776.54026, MR 1216780 |
| Reference:
|
[4] Charatonik J.J., Grabowski Z.: Homotopically fixed arcs and contractibility of dendroids.Fund. Math. 100 (1978), 229-239. MR 0509549 |
| Reference:
|
[5] Charatonik J.J., Lee T.J., Omiljanowski K.: Interrelations between some noncontractibility conditions.Rend. Circ. Mat. Palermo 41 (1992), 31-54. Zbl 0795.54048, MR 1175586 |
| Reference:
|
[6] Czuba S.T.: R-continua and contractibility of dendroids.Bull. Acad. Polon. Sci. Ser. Sci. Math. 27 (1979), 299-302. Zbl 0424.54026, MR 0552053 |
| Reference:
|
[7] Fitzpatrick B., Jr., Lelek A.: Some local properties of Suslinian compacta.Colloq. Math. 31 (1974), 189-197. Zbl 0292.54036, MR 0367943 |
| Reference:
|
[8] Hopf H., Pannwitz E.: Über stetige Deformationen von Komplexen in sich.Math. Ann. 108 (1933), 433-465. Zbl 0006.42203, MR 1512859 |
| Reference:
|
[9] Lelek A.: Strongly homotopically stabile points.Colloq. Math. 37 (1977), 193-203. Zbl 0376.55012, MR 0474234 |
| Reference:
|
[10] Nadler S.B., Jr.: Continuum Theory.M. Dekker (1992). Zbl 0757.54009, MR 1192552 |
| Reference:
|
[11] Oversteegen L.G.: Non-contractibility of continua.Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 26 (1978), 837-840. Zbl 0404.54031, MR 0518989 |
| . |
