# Homotopy properties of curves

Janusz Jerzy Charatonik; Alejandro Illanes

Commentationes Mathematicae Universitatis Carolinae (1998)

- Volume: 39, Issue: 3, page 573-580
- ISSN: 0010-2628

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topCharatonik, Janusz Jerzy, and Illanes, Alejandro. "Homotopy properties of curves." Commentationes Mathematicae Universitatis Carolinae 39.3 (1998): 573-580. <http://eudml.org/doc/248246>.

@article{Charatonik1998,

abstract = {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.},

author = {Charatonik, Janusz Jerzy, Illanes, Alejandro},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {continuum; contractible; curve; deformation; dendroid; fixed; homotopy; steady; contractible curve; deformation; dendroid; homotopy; steady},

language = {eng},

number = {3},

pages = {573-580},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Homotopy properties of curves},

url = {http://eudml.org/doc/248246},

volume = {39},

year = {1998},

}

TY - JOUR

AU - Charatonik, Janusz Jerzy

AU - Illanes, Alejandro

TI - Homotopy properties of curves

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1998

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 39

IS - 3

SP - 573

EP - 580

AB - 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.

LA - eng

KW - continuum; contractible; curve; deformation; dendroid; fixed; homotopy; steady; contractible curve; deformation; dendroid; homotopy; steady

UR - http://eudml.org/doc/248246

ER -

## References

top- Borsuk K., Jaworowski J.W., On labil and stabil points, Fund. Math. 39 (1952), 159-175. (1952) MR0056283
- 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. (1977) Zbl0373.54029MR0464197
- Charatonik J.J., Contractibility of curves, Matematiche (Catania) 46 (1991), 559-592. (1991) Zbl0776.54026MR1216780
- Charatonik J.J., Grabowski Z., Homotopically fixed arcs and contractibility of dendroids, Fund. Math. 100 (1978), 229-239. (1978) MR0509549
- Charatonik J.J., Lee T.J., Omiljanowski K., Interrelations between some noncontractibility conditions, Rend. Circ. Mat. Palermo 41 (1992), 31-54. (1992) Zbl0795.54048MR1175586
- Czuba S.T., R-continua and contractibility of dendroids, Bull. Acad. Polon. Sci. Ser. Sci. Math. 27 (1979), 299-302. (1979) Zbl0424.54026MR0552053
- Fitzpatrick B., Jr., Lelek A., Some local properties of Suslinian compacta, Colloq. Math. 31 (1974), 189-197. (1974) Zbl0292.54036MR0367943
- Hopf H., Pannwitz E., Über stetige Deformationen von Komplexen in sich, Math. Ann. 108 (1933), 433-465. (1933) Zbl0006.42203MR1512859
- Lelek A., Strongly homotopically stabile points, Colloq. Math. 37 (1977), 193-203. (1977) Zbl0376.55012MR0474234
- Nadler S.B., Jr., Continuum Theory, M. Dekker (1992). (1992) Zbl0757.54009MR1192552
- Oversteegen L.G., Non-contractibility of continua, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 26 (1978), 837-840. (1978) Zbl0404.54031MR0518989

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