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)



Refinable maps and $ \theta\sb n$-continua

Authors: E. E. Grace and Eldon J. Vought
Journal: Proc. Amer. Math. Soc. 106 (1989), 231-239
MSC: Primary 54C10; Secondary 54B15, 54C20, 54E45, 54G20
MathSciNet review: 964455
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Many properties of continua, e.g., irreducibility, span zero, and various kinds of aposyndesis and unicoherence, are preserved by refinable maps or their inverses. The purpose of this paper is to consider the extent to which the property of being a $ {\theta '_n}$-continuum is preserved by refinable maps or by inverses of refinable maps. One consequence of this study is to generalize results of the first author where the domain or range is a graph. Several of his results are corollaries of ours.

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

  • [1] R. W. FitzGerald, Connected sets with a finite disconnection property, 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. 139-173. MR 0365478 (51:1730)
  • [2] J. Ford and J. W. Rogers, Jr., Refinable maps, Colloq. Math. 39 (1978), 263-269. MR 522365 (80d:54009)
  • [3] E. E. Grace, Refinable maps on graphs are near homeomorphisms, Top. Proc. 2 (1977), 139-150. MR 540601 (80m:54022)
  • [4] E. E. Grace and E. J. Vought, Monotone decompositions of $ {\theta _n}$-continua, Trans. Amer. Math. Soc. 263 (1981), 261-270. MR 590423 (81k:54058)
  • [5] -, Quasi-monotone mappings on $ {\theta _n}$-continua, Topology and its Applications 17 (1984), 55-62.
  • [6] H. Hosokawa, Aposyndesis and coherence of continua under refinable maps, Tsukuba J. Math. 7 (1983), 367-372. MR 723864 (85f:54069)
  • [7] F. B. Jones, Concerning non-aposyndetic continua, Amer. J. Math. 70 (1948), 403-413. MR 0025161 (9:606h)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54C10, 54B15, 54C20, 54E45, 54G20

Retrieve articles in all journals with MSC: 54C10, 54B15, 54C20, 54E45, 54G20

Additional Information

Keywords: Refinable map, $ {\theta _n}$-continuum, $ {\theta '_n}$-continuum, tranche, quotient space, induced map, graph, near homeomorphism
Article copyright: © Copyright 1989 American Mathematical Society

American Mathematical Society