Homotopy properties of curves

Janusz Jerzy Charatonik; Alejandro Illanes

Commentationes Mathematicae Universitatis Carolinae (1998)

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

Abstract

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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.

How to cite

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Charatonik, 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

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  1. Borsuk K., Jaworowski J.W., On labil and stabil points, Fund. Math. 39 (1952), 159-175. (1952) MR0056283
  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. (1977) Zbl0373.54029MR0464197
  3. Charatonik J.J., Contractibility of curves, Matematiche (Catania) 46 (1991), 559-592. (1991) Zbl0776.54026MR1216780
  4. Charatonik J.J., Grabowski Z., Homotopically fixed arcs and contractibility of dendroids, Fund. Math. 100 (1978), 229-239. (1978) MR0509549
  5. Charatonik J.J., Lee T.J., Omiljanowski K., Interrelations between some noncontractibility conditions, Rend. Circ. Mat. Palermo 41 (1992), 31-54. (1992) Zbl0795.54048MR1175586
  6. Czuba S.T., R-continua and contractibility of dendroids, Bull. Acad. Polon. Sci. Ser. Sci. Math. 27 (1979), 299-302. (1979) Zbl0424.54026MR0552053
  7. Fitzpatrick B., Jr., Lelek A., Some local properties of Suslinian compacta, Colloq. Math. 31 (1974), 189-197. (1974) Zbl0292.54036MR0367943
  8. Hopf H., Pannwitz E., Über stetige Deformationen von Komplexen in sich, Math. Ann. 108 (1933), 433-465. (1933) Zbl0006.42203MR1512859
  9. Lelek A., Strongly homotopically stabile points, Colloq. Math. 37 (1977), 193-203. (1977) Zbl0376.55012MR0474234
  10. Nadler S.B., Jr., Continuum Theory, M. Dekker (1992). (1992) Zbl0757.54009MR1192552
  11. 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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