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)



Can a $ 2$-coherent Peano continuum separate $ E\sp{3}$?

Author: W. C. Chewning
Journal: Proc. Amer. Math. Soc. 30 (1971), 185-188
MSC: Primary 54.55
MathSciNet review: 0288733
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The fact that there are unicoherent continua which separate $ {E^2}$ is well known, e.g., a circle with a spiral converging onto it is such a continuum. In this paper we extend this pathology by describing a Peano continuum which separates $ {E^3}$ and has the property that however it is written as the union of two unicoherent Peano continua, their intersection is unicoherent.

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

  • [1] James Dugundji, Topology, Allyn and Bacon, Inc., Boston, Mass., 1966. MR 0193606
  • [2] S. Eilenberg, Multicoherence. I, Fund. Math. 27 (1936), 153-190.
  • [3] Samuel Eilenberg and Norman Steenrod, Foundations of algebraic topology, Princeton University Press, Princeton, New Jersey, 1952. MR 0050886
  • [4] Witold Hurewicz and Henry Wallman, Dimension Theory, Princeton Mathematical Series, v. 4, Princeton University Press, Princeton, N. J., 1941. MR 0006493
  • [5] W. R. R. Transue, On a definition of connectedness in dimension N, Dissertation Abstracts #67-16, 243, University Microfilms, Ann Arbor, Mich., 1967.
  • [6] Gordon Thomas Whyburn, Analytic topology, American Mathematical Society Colloquium Publications, Vol. XXVIII, American Mathematical Society, Providence, R.I., 1963. MR 0182943

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54.55

Retrieve articles in all journals with MSC: 54.55

Additional Information

Keywords: Unicoherence, 2-coherence, local unicoherence, Čech homology and cohomology
Article copyright: © Copyright 1971 American Mathematical Society

American Mathematical Society