Semilattices on Peano continua
HTML articles powered by AMS MathViewer
- by W. Wiley Williams PDF
- Proc. Amer. Math. Soc. 49 (1975), 495-500 Request permission
Abstract:
A continuum is cell-cyclic if every cyclic element is an $n$-cell for some integer $n$. It is shown that every cell-cyclic Peano continuum admits a topological semilattice.References
-
K. Borsuk, Sur les retracts, Fund. Math. 17 (1931), 164.
—, Theory of retracts, Monografie Mat., Tom 44, PWN, Warsaw, 1967. MR 35 #7306.
- Virginia Knight, A continuous partial order for Peano continua, Pacific J. Math. 30 (1969), 141–153. MR 246266 C. Kuratowski and G. T. Whyburn, Sur les éléments cycliques et leurs applications, Fund. Math. 16 (1930), 305-331.
- Jimmie D. Lawson and Wiley Williams, Topological semilattices and their underlying spaces, Semigroup Forum 1 (1970), no. 3, 209–223. MR 268322, DOI 10.1007/BF02573038
- A. D. Wallace, Acyclicity of compact connected semigroups, Fund. Math. 50 (1961/62), 99–105. MR 132533, DOI 10.4064/fm-50-2-99-105
- Gordon Thomas Whyburn, Analytic Topology, American Mathematical Society Colloquium Publications, Vol. 28, American Mathematical Society, New York, 1942. MR 0007095
- Gordon T. Whyburn, Concerning the Structure of a Continuous Curve, Amer. J. Math. 50 (1928), no. 2, 167–194. MR 1506664, DOI 10.2307/2371754
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 49 (1975), 495-500
- MSC: Primary 54F30; Secondary 54H15
- DOI: https://doi.org/10.1090/S0002-9939-1975-0383374-5
- MathSciNet review: 0383374