Semigroups on acyclic plane continua
HTML articles powered by AMS MathViewer
- by B. E. Wilder PDF
- Proc. Amer. Math. Soc. 28 (1971), 587-589 Request permission
Abstract:
It is shown that an acyclic irreducible plane continuum which admits the structure of a topological semigroup is an arc if it has an identity, and is either an arc, is trivial, or is decomposible into an arc if it satisfies ${M^2} = M$. This extends some results of Friedberg and Mahavier concerning semigroups on chainable continua.References
- R. H. Bing, A simple closed curve is the only homogeneous bounded plane continuum that contains an arc, Canadian J. Math. 12 (1960), 209–230. MR 111001, DOI 10.4153/CJM-1960-018-x
- Haskell Cohen and R. J. Koch, Acyclic semigroups and multiplications on two-manifolds, Trans. Amer. Math. Soc. 118 (1965), 420–427. MR 175098, DOI 10.1090/S0002-9947-1965-0175098-2
- M. Friedberg and W. S. Mahavier, Semigroups on chainable and circle-like continua, Math. Z. 106 (1968), 159–161. MR 231937, DOI 10.1007/BF01110123
- Andrew M. Gleason, Arcs in locally compact groups, Proc. Nat. Acad. Sci. U.S.A. 36 (1950), 663–667. MR 38356, DOI 10.1073/pnas.36.11.663
- R. P. Hunter, Note on arcs in semigroups, Fund. Math. 49 (1960/61), 233–245. MR 123300, DOI 10.4064/fm-49-3-233-245
- Robert J. Koch, Threads in compact semigroups, Math. Z. 86 (1964), 312–316. MR 171268, DOI 10.1007/BF01110405
- R. J. Koch and A. D. Wallace, Admissibility of semigroup structures on continua, Trans. Amer. Math. Soc. 88 (1958), 277–287. MR 95223, DOI 10.1090/S0002-9947-1958-0095223-8
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 28 (1971), 587-589
- MSC: Primary 54.80
- DOI: https://doi.org/10.1090/S0002-9939-1971-0276946-6
- MathSciNet review: 0276946