Revista Integración, temas de matemáticas.

Revista Integración, temas de matemáticas

Vol. 39 No. 1 (2021): Revista integración, temas de matemáticas
Research and Innovation Articles

Mappings between dendroids (fans) that (does not) preserve (non)contractibility.

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  • José G. Anaya,
  • Félix Capulín,
  • Mónica Sánchez Garrido
José G. Anaya
Autonomous Mexico State University
Félix Capulín
Autonomous Mexico State University
Mónica Sánchez Garrido
Autonomous Mexico State University
DOI: https://doi.org/10.18273/revint.v39n1-2021001

Published 2021-05-19

Keywords

  • Ri−continuum,
  • confluent mapping,
  • strongly freely decomposable mapping,
  • freely decomposable mapping,
  • contractibility,
  • Jones’s function T
    • ...More
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How to Cite

Anaya, J. G., Capulín, F., & Sánchez Garrido, M. (2021). Mappings between dendroids (fans) that (does not) preserve (non)contractibility. Revista Integración, Temas De matemáticas, 39(1), 1–22. https://doi.org/10.18273/revint.v39n1-2021001

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Abstract

J. J. Charatonik formulated in 1991 the following problem: What are all mappings that preserve contractibility (noncontractibility) of dendroids? On the other hand, J. J. Charatonik, W. J. Charatonik, and S. Miklos asked in 1990 the following questions (among others related to contractibility): What kinds of confluent mappings preserve contractibility of fans? And what kinds of confluent mappings preserve non contractibility of fans?
In this paper, we will show some partial answers to these questions. Additionally, we will consider these questions with other kinds of families of mappings.

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References

  1. Bellamy D.P. and Charatonik J.J., “The set function T and contractibility of continua”, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys., 25 (1977), No. 1, 47-49.
  2. Camargo J. and Macías S, “On freely decomposable maps”, Top. Appl., 159 (2012), No. 3, 891-899. doi: 10.1016/j.topol.2011.12.006
  3. Capulín F., Illanes A., Orozco F., Puga I. and Pyrih P., “Q−points in fans”, Topology Proc., 36 (2010), 85-105.
  4. Charatonik J.J., “On fans”, Dissertationes Math. (Rozprawy Mat.), 54 (1967), 39.
  5. Charatonik J.J., “Contractibility of curves”, Matematiche (Catania), 46 (1991), No. 2, 559-592.
  6. Charatonik J.J., Charatonik W.J. and Miklos S., “Confluent mappings of fans”, Dissertationes Math. (Rozprawy Mat.), 301 (1990), 86.
  7. Charatonik J.J., Lee T.J. and Omiljanowski K., “Interrelations between some noncontractibility conditions”, Rend. Circ. Mat. Palermo, 41 (1992), No. 1, 31-54. doi: 10.1007/BF02844461
  8. Czuba S.T., “Ri−continua and contractibility”, Proceedings of the International Conference on Geometric Topology, Warszawa (1980), 75-79.
  9. Macías S., Topics on continua, Chapman & Hall/CRC, vol. 275, Boca Raton, FL, 2005. doi: 10.1201/9781420026535
  10. Nadler, S.B. Jr., Continuum theory, Monographs and Textbooks in Pure and Applied Mathematics, 158, Marcel Dekker, Inc., New York, 1992.
  11. Nadler S.B. Jr., Hyperspaces of sets, Monographs and Textbooks in Pure and Applied Mathematics, 49, Marcel Dekker, Inc., New York-Basel, 1978.
  12. Oversteegen L.G., “Internal characterizations of contractibility for fans”, Bull. Acad. Polon. Sci. Sér. Sci. Math., 27 (1979), No. 5, 391-395.
  13. Rhee C.J., Hur K. and Baik B.S., “Ri−sets and contractibility”, J. Korean Math. Soc, 34 (1997), No. 2, 309-319.