Monotone retracts and some characterizations of dendrites
HTML articles powered by AMS MathViewer
- by G. R. Gordh and Lewis Lum PDF
- Proc. Amer. Math. Soc. 59 (1976), 156-158 Request permission
Abstract:
Let $M$ be a metric continuum containing a fixed point $p$. The following conditions are shown to be equivalent. (i) $M$ is a dendrite. (ii) Each subcontinuum of $M$ is a monotone retract of $M$. (iii) $M$ is arcwise connected and each subcontinuum of $M$ containing $p$ is a monotone retract of $M$.References
- G. R. Gordh Jr., Concerning closed quasi-orders on hereditarily unicoherent continua, Fund. Math. 78 (1973), no. 1, 61–73. MR 322835, DOI 10.4064/fm-78-1-61-73
- John G. Hocking and Gail S. Young, Topology, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1961. MR 0125557
- Lewis Lum, A characterization of local connectivity in dendroids, Studies in topology (Proc. Conf., Univ. North Carolina, Charlotte, N.C., 1974; dedicated to Math. Sect. Polish Acad. Sci.), Academic Press, New York, 1975, pp. 331–338. MR 0358739 —, Order preserving and monotone retracts of a dendroid (submitted). L. E. Rogers, Arcwise connectedness and continuum chainability (submitted).
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 59 (1976), 156-158
- MSC: Primary 54F20
- DOI: https://doi.org/10.1090/S0002-9939-1976-0423317-X
- MathSciNet review: 0423317