Previous |  Up |  Next

Article

Title: Extending generalized Whitney maps (English)
Author: Lončar, Ivan
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 53
Issue: 2
Year: 2017
Pages: 65-76
Summary lang: English
.
Category: math
.
Summary: 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. (English)
Keyword: extending generalized Whitney map
Keyword: hyperspace
MSC: 54B20
MSC: 54F15
idZBL: Zbl 06770052
idMR: MR3672781
DOI: 10.5817/AM2017-2-65
.
Date available: 2017-06-09T07:47:50Z
Last updated: 2020-01-05
Stable URL: http://hdl.handle.net/10338.dmlcz/146793
.
Reference: [1] Charatonik, J.J., Charatonik, W.J.: Whitney maps—a non-metric case.Colloq. Math. 83 (2) (2000), 305–307. Zbl 0953.54013, MR 1758323
Reference: [2] Engelking, R.: General Topology.PWN Warszawa, 1977. Zbl 0373.54002, MR 0500780
Reference: [3] Illanes, A., Nadler, Jr., S.B.: Hyperspaces: Fundamentals and Recent advances.Marcel Dekker, New York-Basel, 1999. Zbl 0933.54009, MR 1670250
Reference: [4] Jones, F.B.: Aposyndetic continua and certain boundary problems.Amer. J. Math. 63 (1941), 545–553. Zbl 0025.24003, MR 0004771, 10.2307/2371367
Reference: [5] Kelley, J.L.: Hyperspaces of a continuum.Trans. Amer. Math. Soc. 52 (1942), 22–36. Zbl 0061.40107, MR 0006505, 10.1090/S0002-9947-1942-0006505-8
Reference: [6] Lončar, I.: Non-metric rim-metrizable continua and unique hyperspace.Publ. Inst. Math. (Beograd) (N.S.) 73 (87) (2003), 97–113. Zbl 1054.54026, MR 2068242, 10.2298/PIM0373097L
Reference: [7] Michael, E.: Topologies on spaces of subsets.Trans. Amer. Math. Soc. 71 (1951), 152–182. Zbl 0043.37902, MR 0042109, 10.1090/S0002-9947-1951-0042109-4
Reference: [8] Nadler, S.B.: Hyperspaces of sets.Marcel Dekker, Inc., New York, 1978. Zbl 0432.54007, MR 0500811
Reference: [9] Nadler, S.B.: Continuum theory.Marcel Dekker, Inc., New York, 1992. Zbl 0757.54009, MR 1192552
Reference: [10] Smith, M., Stone, J.: On non-metric continua that support Whitney maps.Topology Appl. 170 (2014), 63–85. Zbl 1296.54037, MR 3200390, 10.1016/j.topol.2014.02.007
Reference: [11] Stone, J.: Non-metric continua that support Whitney maps.Dissertation. Zbl 1296.54037
Reference: [12] Ward, L.E.: Extending Whitney maps.Pacific J. Math. 93 (1981), 465–470. Zbl 0457.54008, MR 0623577, 10.2140/pjm.1981.93.465
Reference: [13] Whitney, H.: Regular families of curves, I.Proc. Nat. Acad. Sci. 18 (1932), 275–278. Zbl 0004.07503, 10.1073/pnas.18.3.275
Reference: [14] Whitney, H.: Regular families of curves.Ann. of Math. (2) 34 (1933), 244–270. Zbl 0006.37101, MR 1503106, 10.2307/1968202
Reference: [15] Wilder, B.E.: Between aposyndetic and indecomposable continua.Topology Proc. 17 (1992), 325–331. Zbl 0788.54041, MR 1255815
.

Files

Files Size Format View
ArchMathRetro_053-2017-2_1.pdf 525.4Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo