Extending generalized Whitney maps

Ivan Lončar

Archivum Mathematicum (2017)

  • Volume: 053, Issue: 2, page 65-76
  • ISSN: 0044-8753

Abstract

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For metrizable continua, there exists the well-known notion of a Whitney map. If is a nonempty, compact, and metric space, then any Whitney map for any closed subset of can be extended to a Whitney map for [3, 16.10 Theorem]. The main purpose of this paper is to prove some generalizations of this theorem.

How to cite

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Lončar, Ivan. "Extending generalized Whitney maps." Archivum Mathematicum 053.2 (2017): 65-76. <http://eudml.org/doc/288188>.

@article{Lončar2017,
abstract = {For metrizable continua, there exists the well-known notion of a Whitney map. If $X$ is a nonempty, compact, and metric space, then any Whitney map for any closed subset of $2^\{X\}$ can be extended to a Whitney map for $2^\{X\}$ [3, 16.10 Theorem]. The main purpose of this paper is to prove some generalizations of this theorem.},
author = {Lončar, Ivan},
journal = {Archivum Mathematicum},
keywords = {extending generalized Whitney map; hyperspace},
language = {eng},
number = {2},
pages = {65-76},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Extending generalized Whitney maps},
url = {http://eudml.org/doc/288188},
volume = {053},
year = {2017},
}

TY - JOUR
AU - Lončar, Ivan
TI - Extending generalized Whitney maps
JO - Archivum Mathematicum
PY - 2017
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 053
IS - 2
SP - 65
EP - 76
AB - For metrizable continua, there exists the well-known notion of a Whitney map. If $X$ is a nonempty, compact, and metric space, then any Whitney map for any closed subset of $2^{X}$ can be extended to a Whitney map for $2^{X}$ [3, 16.10 Theorem]. The main purpose of this paper is to prove some generalizations of this theorem.
LA - eng
KW - extending generalized Whitney map; hyperspace
UR - http://eudml.org/doc/288188
ER -

References

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  1. Charatonik, J.J., Charatonik, W.J., Whitney maps—a non-metric case, Colloq. Math. 83 (2) (2000), 305–307. (2000) Zbl0953.54013MR1758323
  2. Engelking, R., General Topology, PWN Warszawa, 1977. (1977) Zbl0373.54002MR0500780
  3. Illanes, A., Nadler, Jr., S.B., Hyperspaces: Fundamentals and Recent advances, Marcel Dekker, New York-Basel, 1999. (1999) Zbl0933.54009MR1670250
  4. Jones, F.B., 10.2307/2371367, Amer. J. Math. 63 (1941), 545–553. (1941) Zbl0025.24003MR0004771DOI10.2307/2371367
  5. Kelley, J.L., 10.1090/S0002-9947-1942-0006505-8, Trans. Amer. Math. Soc. 52 (1942), 22–36. (1942) Zbl0061.40107MR0006505DOI10.1090/S0002-9947-1942-0006505-8
  6. Lončar, I., 10.2298/PIM0373097L, Publ. Inst. Math. (Beograd) (N.S.) 73 (87) (2003), 97–113. (2003) Zbl1054.54026MR2068242DOI10.2298/PIM0373097L
  7. Michael, E., 10.1090/S0002-9947-1951-0042109-4, Trans. Amer. Math. Soc. 71 (1951), 152–182. (1951) Zbl0043.37902MR0042109DOI10.1090/S0002-9947-1951-0042109-4
  8. Nadler, S.B., Hyperspaces of sets, Marcel Dekker, Inc., New York, 1978. (1978) Zbl0432.54007MR0500811
  9. Nadler, S.B., Continuum theory, Marcel Dekker, Inc., New York, 1992. (1992) Zbl0757.54009MR1192552
  10. Smith, M., Stone, J., 10.1016/j.topol.2014.02.007, Topology Appl. 170 (2014), 63–85. (2014) Zbl1296.54037MR3200390DOI10.1016/j.topol.2014.02.007
  11. Stone, J., Non-metric continua that support Whitney maps, Dissertation. Zbl1296.54037
  12. Ward, L.E., 10.2140/pjm.1981.93.465, Pacific J. Math. 93 (1981), 465–470. (1981) Zbl0457.54008MR0623577DOI10.2140/pjm.1981.93.465
  13. Whitney, H., 10.1073/pnas.18.3.275, Proc. Nat. Acad. Sci. 18 (1932), 275–278. (1932) Zbl0004.07503DOI10.1073/pnas.18.3.275
  14. Whitney, H., 10.2307/1968202, Ann. of Math. (2) 34 (1933), 244–270. (1933) Zbl0006.37101MR1503106DOI10.2307/1968202
  15. Wilder, B.E., Between aposyndetic and indecomposable continua, Topology Proc. 17 (1992), 325–331. (1992) Zbl0788.54041MR1255815

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