Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Arcwise connectedness of semiaposyndetic plane continua


Author: Charles L. Hagopian
Journal: Trans. Amer. Math. Soc. 158 (1971), 161-165
MSC: Primary 54.55
DOI: https://doi.org/10.1090/S0002-9947-1971-0284981-1
MathSciNet review: 0284981
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In a recent paper, the author proved that if a compact plane continuum $ M$ contains a finite point set $ F$ such that, for each point $ x$ in $ M - F,M$ is semi-locally-connected and not aposyndetic at $ x$, then $ M$ is arcwise connected. The primary purpose of this paper is to generalize that theorem. Semiaposyndesis, a generalization of semi-local-connectedness, is defined and arcwise connectedness is established for certain semiaposyndetic plane continua.


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

  • [1] C. L. Hagopian, Concerning arcwise connectedness and the existence of simple closed curves in plane continua, Trans. Amer. Math. Soc. 147 (1970), 389-402. MR 40 #8030. MR 0254823 (40:8030)
  • [2] -, A cut point theorem for plane continua, Duke Math. J. (to appear). MR 0284980 (44:2204)
  • [3] -, Concerning the cyclic connectivity of plane continua, Michigan Math. J. (to appear). MR 0300248 (45:9294)
  • [4] F. B. Jones, Aposyndetic continua and certain boundary problems, Amer. J. Math. 63 (1941), 545-553. MR 3, 59. MR 0004771 (3:59e)
  • [5] -, A characterization of a semi-locally-connected plane continuum, Bull. Amer. Math. Soc. 53 (1947), 170-175. MR 8, 397. MR 0019301 (8:397e)
  • [6] -, Concerning non-aposyndetic continua, Amer. J. Math. 70 (1948), 403-413. MR 9, 606. MR 0025161 (9:606h)
  • [7] -, Problems in the plane, Summary of Lectures and Seminars, Summer Institute on Set Theoretic Topology, Madison, Wisconsin 1955; revised 1957, pp. 70-71.
  • [8] R. L. Moore, Foundations of point set theory, rev. ed., Amer. Math. Soc. Colloq. Publ., vol. 13, Amer. Math. Soc., Providence, R. I., 1962. MR 0150722 (27:709)
  • [9] G. T. Whyburn, Semi-locally connected sets, Amer. J. Math. 61 (1939), 733-749. MR 1, 31. MR 0000182 (1:31c)
  • [10] -, Analytic topology, rev. ed., Amer. Math. Soc. Colloq. Publ., vol. 28, Amer. Math. Soc., Providence, R. I., 1963. MR 32 #425.

Similar Articles

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

Retrieve articles in all journals with MSC: 54.55


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1971-0284981-1
Keywords: Semiaposyndesis, semi-local-connectedness, aposyndesis, arcwise connected continua, folded complementary domain
Article copyright: © Copyright 1971 American Mathematical Society

American Mathematical Society