$\epsilon$-selections
HTML articles powered by AMS MathViewer
- by Sam B. Nadler
- Proc. Amer. Math. Soc. 114 (1992), 287-293
- DOI: https://doi.org/10.1090/S0002-9939-1992-1074756-7
- PDF | Request permission
Abstract:
Some complete and some partial characterizations of continua are obtained in terms of the existence of an $\varepsilon$-selection on one or another of their hyperspaces for each $\varepsilon > 0$.References
- R. H. Bing, Snake-like continua, Duke Math. J. 18 (1951), 653–663. MR 43450
- Karol Borsuk, Theory of retracts, Monografie Matematyczne, Tom 44, Państwowe Wydawnictwo Naukowe, Warsaw, 1967. MR 0216473
- C. E. Capel and W. L. Strother, Multi-valued functions and partial order, Portugal. Math. 17 (1958), 41–47. MR 101512
- J. B. Fugate, Retracting fans onto finite fans, Fund. Math. 71 (1971), no. 2, 113–125. MR 296904, DOI 10.4064/fm-71-2-113-125
- J. B. Fugate, Small retractions of smooth dendroids onto trees, Fund. Math. 71 (1971), no. 3, 255–262. MR 296906, DOI 10.4064/fm-71-3-255-262
- K. Kuratowski, Topology. Vol. II, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe [Polish Scientific Publishers], Warsaw, 1968. New edition, revised and augmented; Translated from the French by A. Kirkor. MR 0259835
- K. Kuratowski, S. B. Nadler Jr., and G. S. Young, Continuous selections on locally compact separable metric spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 18 (1970), 5–11 (English, with Russian summary). MR 264630
- Ernest Michael, Topologies on spaces of subsets, Trans. Amer. Math. Soc. 71 (1951), 152–182. MR 42109, DOI 10.1090/S0002-9947-1951-0042109-4
- 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. and L. E. Ward Jr., Concerning continuous selections, Proc. Amer. Math. Soc. 25 (1970), 369–374. MR 256360, DOI 10.1090/S0002-9939-1970-0256360-9
- R. H. Sorgenfrey, Concerning triodic continua, Amer. J. Math. 66 (1944), 439–460. MR 10968, DOI 10.2307/2371908
Bibliographic Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 114 (1992), 287-293
- MSC: Primary 54B20; Secondary 54C65, 54F15
- DOI: https://doi.org/10.1090/S0002-9939-1992-1074756-7
- MathSciNet review: 1074756