Geodesic
Extending generalized Whitney maps
Archivum mathematicum, Tome 53 (2017) no. 2, pp. 65-76
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
DOI : 10.5817/AM2017-2-65
Classification : 54B20, 54F15
Keywords: extending generalized Whitney map; hyperspace 
@article{10_5817_AM2017_2_65,
     author = {Lon\v{c}ar, Ivan},
     title = {Extending generalized {Whitney} maps},
     journal = {Archivum mathematicum},
     pages = {65--76},
     year = {2017},
     volume = {53},
     number = {2},
     doi = {10.5817/AM2017-2-65},
     mrnumber = {3672781},
     zbl = {06770052},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5817/AM2017-2-65/}
}
TY  - JOUR
AU  - Lončar, Ivan
TI  - Extending generalized Whitney maps
JO  - Archivum mathematicum
PY  - 2017
SP  - 65
EP  - 76
VL  - 53
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.5817/AM2017-2-65/
DO  - 10.5817/AM2017-2-65
LA  - en
ID  - 10_5817_AM2017_2_65
ER  - 
%0 Journal Article
%A Lončar, Ivan
%T Extending generalized Whitney maps
%J Archivum mathematicum
%D 2017
%P 65-76
%V 53
%N 2
%U http://geodesic.mathdoc.fr/articles/10.5817/AM2017-2-65/
%R 10.5817/AM2017-2-65
%G en
%F 10_5817_AM2017_2_65
Lončar, Ivan. Extending generalized Whitney maps. Archivum mathematicum, Tome 53 (2017) no. 2, pp. 65-76. doi: 10.5817/AM2017-2-65

[1] Charatonik, J.J., Charatonik, W.J.: Whitney maps—a non-metric case. Colloq. Math. 83 (2) (2000), 305–307. | MR | Zbl

[2] Engelking, R.: General Topology. PWN Warszawa, 1977. | MR | Zbl

[3] Illanes, A., Nadler, Jr., S.B.: Hyperspaces: Fundamentals and Recent advances. Marcel Dekker, New York-Basel, 1999. | MR | Zbl

[4] Jones, F.B.: Aposyndetic continua and certain boundary problems. Amer. J. Math. 63 (1941), 545–553. | DOI | MR | Zbl

[5] Kelley, J.L.: Hyperspaces of a continuum. Trans. Amer. Math. Soc. 52 (1942), 22–36. | DOI | MR | Zbl

[6] Lončar, I.: Non-metric rim-metrizable continua and unique hyperspace. Publ. Inst. Math. (Beograd) (N.S.) 73 (87) (2003), 97–113. | DOI | MR | Zbl

[7] Michael, E.: Topologies on spaces of subsets. Trans. Amer. Math. Soc. 71 (1951), 152–182. | DOI | MR | Zbl

[8] Nadler, S.B.: Hyperspaces of sets. Marcel Dekker, Inc., New York, 1978. | MR | Zbl

[9] Nadler, S.B.: Continuum theory. Marcel Dekker, Inc., New York, 1992. | MR | Zbl

[10] Smith, M., Stone, J.: On non-metric continua that support Whitney maps. Topology Appl. 170 (2014), 63–85. | DOI | MR | Zbl

[11] Stone, J.: Non-metric continua that support Whitney maps. Dissertation. | Zbl

[12] Ward, L.E.: Extending Whitney maps. Pacific J. Math. 93 (1981), 465–470. | DOI | MR | Zbl

[13] Whitney, H.: Regular families of curves, I. Proc. Nat. Acad. Sci. 18 (1932), 275–278. | DOI | Zbl

[14] Whitney, H.: Regular families of curves. Ann. of Math. (2) 34 (1933), 244–270. | DOI | MR | Zbl

[15] Wilder, B.E.: Between aposyndetic and indecomposable continua. Topology Proc. 17 (1992), 325–331. | MR | Zbl

Cité par Sources :