Whitney continua of curves
HTML articles powered by AMS MathViewer
- by Hisao Kato
- Trans. Amer. Math. Soc. 300 (1987), 367-381
- DOI: https://doi.org/10.1090/S0002-9947-1987-0871681-1
- PDF | Request permission
Abstract:
In this paper, we prove several theorems relating shape properties of Whitney continua of curves. In particular, we investigate the fundamental dimension and the shape type of Whitney continua of curves.References
- K. Borsuk, Theory of shape, Lecture Notes Series, No. 28, Aarhus Universitet, Matematisk Institut, Aarhus, 1971. MR 0293602
- J. H. Case and R. E. Chamberlin, Characterizations of tree-like continua, Pacific J. Math. 10 (1960), 73–84. MR 111000
- R. Duda, On the hyperspace of subcontinua of a finite graph. I, Fund. Math. 62 (1968), 265–286. MR 236881, DOI 10.4064/fm-62-3-265-286
- R. Duda, Correction to the paper: “On the hyperspace of subcontinua of a finite graph. I”, Fund. Math. 69 (1970), 207–211. MR 273575, DOI 10.4064/fm-69-3-207-211
- Doug Curtis, Stable points in hyperspaces of Peano continua, Proceedings of the 1985 topology conference (Tallahassee, Fla., 1985), 1985, pp. 259–276. MR 876898
- Jack T. Goodykoontz Jr. and Sam B. Nadler Jr., Whitney levels in hyperspaces of certain Peano continua, Trans. Amer. Math. Soc. 274 (1982), no. 2, 671–694. MR 675074, DOI 10.1090/S0002-9947-1982-0675074-7
- Hisao Kato, Concerning hyperspaces of certain Peano continua and strong regularity of Whitney maps, Pacific J. Math. 119 (1985), no. 1, 159–167. MR 797021
- Hisao Kato, Shape properties of Whitney maps for hyperspaces, Trans. Amer. Math. Soc. 297 (1986), no. 2, 529–546. MR 854083, DOI 10.1090/S0002-9947-1986-0854083-2
- J. L. Kelley, Hyperspaces of a continuum, Trans. Amer. Math. Soc. 52 (1942), 22–36. MR 6505, DOI 10.1090/S0002-9947-1942-0006505-8
- J. Krasinkiewicz, On the hyperspaces of snake-like and circle-like continua, Fund. Math. 83 (1974), no. 2, 155–164. MR 418058, DOI 10.4064/fm-83-2-155-164
- J. Krasinkiewicz, Shape properties of hyperspaces, Fund. Math. 101 (1978), no. 1, 79–91. MR 512244, DOI 10.4064/fm-101-1-79-91
- J. Krasinkiewicz and Sam B. Nadler Jr., Whitney properties, Fund. Math. 98 (1978), no. 2, 165–180. MR 467691, DOI 10.4064/fm-98-2-165-180
- Sibe Mardešić and Jack Segal, Shape theory, North-Holland Mathematical Library, vol. 26, North-Holland Publishing Co., Amsterdam-New York, 1982. The inverse system approach. MR 676973 M. Lynch, Whitney levels in ${C_p}(X)$ are absolute retracts, preprint.
- Sam B. Nadler Jr., Hyperspaces of sets, Monographs and Textbooks in Pure and Applied Mathematics, Vol. 49, Marcel Dekker, Inc., New York-Basel, 1978. A text with research questions. MR 0500811
- Sam B. Nadler Jr., Whitney-reversible properties, Fund. Math. 109 (1980), no. 3, 235–248. MR 597070, DOI 10.4064/fm-109-3-235-248
- Ann Petrus, Contractibility of Whitney continua in $C(X)$, General Topology Appl. 9 (1978), no. 3, 275–288. MR 510909, DOI 10.1016/0016-660x(78)90031-4
- James T. Rogers Jr., The cone = hyperspace property, Canadian J. Math. 24 (1972), 279–285. MR 295302, DOI 10.4153/CJM-1972-022-8
- James T. Rogers Jr., Continua with cones homeomorphic to hyperspaces, General Topology and Appl. 3 (1973), 283–289. MR 362257
- James T. Rogers Jr., Dimension and the Whitney subcontinua of $C(X)$, General Topology and Appl. 6 (1976), no. 1, 91–100. MR 420536
- James T. Rogers Jr., Embedding the hyperspaces of circle-like plane continua, Proc. Amer. Math. Soc. 29 (1971), 165–168. MR 273578, DOI 10.1090/S0002-9939-1971-0273578-0
- James T. Rogers Jr., Hyperspaces of arc-like and circle-like continua, Topology Conference (Virginia Polytech. Inst. and State Univ., Blacksburg, Va., 1973) Lecture Notes in Math., Vol. 375, Springer, Berlin, 1974, pp. 231–235. MR 0356001 —, Whitney continua in the hyperspaces $C(X)$, Pacific J. Math. 58 (1975), 569-584.
- James T. Rogers Jr., Applications of a Vietoris-Begle theorem for multi-valued maps to the cohomology of hyperspaces, Michigan Math. J. 22 (1975), no. 4, 315–319 (1976). MR 397678
- Jack Segal, Hyperspaces of the inverse limit space, Proc. Amer. Math. Soc. 10 (1959), 706–709. MR 108780, DOI 10.1090/S0002-9939-1959-0108780-6
- L. E. Ward Jr., Extending Whitney maps, Pacific J. Math. 93 (1981), no. 2, 465–469. MR 623577 H. Whitney, Regular families of curves. I, Proc. Nat. Acad. Sci. U.S.A. 18 (1939), 184-192.
- Sławomir Nowak, Some properties of fundamental dimension, Fund. Math. 85 (1974), 211–227. MR 383344, DOI 10.4064/fm-85-3-211-227
Bibliographic Information
- © Copyright 1987 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 300 (1987), 367-381
- MSC: Primary 54B20; Secondary 54F43
- DOI: https://doi.org/10.1090/S0002-9947-1987-0871681-1
- MathSciNet review: 871681