Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Semilattices on Peano continua


Author: W. Wiley Williams
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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] K. Borsuk, Sur les retracts, Fund. Math. 17 (1931), 164.
  • [2] -, Theory of retracts, Monografie Mat., Tom 44, PWN, Warsaw, 1967. MR 35 #7306.
  • [3] V. Knight, A continuous partial order for Peano continua, Pacific J. Math. 30 (1969), 141-153. MR 39 #7570. MR 0246266 (39:7570)
  • [4] C. Kuratowski and G. T. Whyburn, Sur les éléments cycliques et leurs applications, Fund. Math. 16 (1930), 305-331.
  • [5] J. D. Lawson and W. W. Williams, Topological semilattices and their underlying spaces, Semigroup Forum 1 (1970), no. 3, 209-223. MR 42 #3221. MR 0268322 (42:3221)
  • [6] A. D. Wallace, Acyclicity of compact connected semigroups, Fund. Math. 50 (1961/62), 99-105. MR 24 #A2373. MR 0132533 (24:A2373)
  • [7] G. T. Whyburn, Analytic topology, Amer. Math. Soc. Colloq. Publ., vol. 28, Amer. Math. Soc., Providence, R. I., 1942. MR 4, 86. MR 0007095 (4:86b)
  • [8] -, Concerning the structure of the continuous curve, Amer. J. Math. 50 (1928), 167-194. MR 1506664

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54F30, 54H15

Retrieve articles in all journals with MSC: 54F30, 54H15


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0383374-5
Keywords: Peano continuum, cyclic element, cell-cyclic, topological semilattice, retract
Article copyright: © Copyright 1975 American Mathematical Society

American Mathematical Society