A new characterization of trees
HTML articles powered by AMS MathViewer
- by L. E. Ward PDF
- Proc. Amer. Math. Soc. 104 (1988), 1252-1255 Request permission
Abstract:
It is proved that a continuum is a tree if and only if for each pair of nondegenerate subcontinua $K$ and $L$ with $K \subset L$, it follows that $K$ contains a cutpoint of $L$.References
- H. Kok, Connected orderable spaces, Mathematical Centre Tracts, No. 49, Mathematisch Centrum, Amsterdam, 1973. MR 0339099
- Karl Menger, Kurventheorie, 2nd ed., Chelsea Publishing Co., Bronx, N.Y., 1967 (German). Herausgegeben unter Mitarbeit von Georg Nöbeling. MR 0221475 R. L. Moore, Concerning the cutpoints of continuous curves and other closed and connected point-sets, Proc. Nat. Acad. Sci. U.S.A. 9 (1923), 101-106.
- L. E. Ward Jr., Recent developments in dendritic spaces and related topics, 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. 601–647. MR 0362267
- Gordon Thomas Whyburn, Analytic Topology, American Mathematical Society Colloquium Publications, Vol. 28, American Mathematical Society, New York, 1942. MR 0007095 R. L. Wilder, Concerning continuous curves, Fund. Math. 7 (1925), 340-377.
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 104 (1988), 1252-1255
- MSC: Primary 54F20; Secondary 54F50, 54F55, 54F65
- DOI: https://doi.org/10.1090/S0002-9939-1988-0969056-6
- MathSciNet review: 969056