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)

 
 

 

Every contractible fan is locally connected at its vertex


Author: Lex G. Oversteegen
Journal: Trans. Amer. Math. Soc. 260 (1980), 379-402
MSC: Primary 54F20; Secondary 54F25
DOI: https://doi.org/10.1090/S0002-9947-1980-0574786-1
MathSciNet review: 574786
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove that each contractible fan is locally connected at its vertex. It follows that every contractible fan is embeddable in the plane. This gives a solution to a problem raised by J. J. Charatonik and C. A. Eberhart.


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

  • [1] David P. Bellamy and J. J. Charatonik, The set function T and contractibility of continua, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 25 (1977), 47-49. MR 0500858 (58:18370)
  • [2] K. Borsuk, A countable broom which can not be imbedded in the plane, Colloq. Math. 10 (1963), 233-236. MR 0155300 (27:5235)
  • [3] J. J. Charatonik and C. A. Eberhart, On contractible dendroids, Colloq. Math. 25 (1972), 89-98. MR 0309082 (46:8193)
  • [4] J. J. Charatonik, Problems and remarks on contractibility of curves, General Topology and Its Relations to Modern Analysis and Algebra. IV, Part B, Assoc. of Czechoslovak Math. and Phys. (Proc. Fourth Prague Topological Sympos., Prague, 1976), Prague, 1977. MR 0464197 (57:4132)
  • [5] J. J. Charatonik and Z. Grabowski, Homotopically fixed arcs and the contractibility of dendroids, Fund. Math. 100 (1978), 229-237. MR 509549 (80c:54042)
  • [6] G. B. Graham, On contractible fans, Doctoral Dissertation, Univ. of California, Riverside, Calif., 1977.
  • [7] K. Kuratowski, Topology, Vol. II, Academic Press, New York, 1968. MR 0259835 (41:4467)
  • [8] J. Mioduszewski, Everywhere oscillating functions, extension of the uniformization and homogeneity of the pseudo-arc, Fund. Math. 56 (1964), 131-155. MR 0176452 (31:724)
  • [9] Lex G. Oversteegen, Non-contractibility of continua, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 26 (1978), 837-840. MR 518989 (80e:54045)
  • [10] -, Fans and embeddings in the plane, Pacific J. Math. 83 (1979), 495-503. MR 557948 (80m:54052)
  • [11] -, Properties of contractible fans, Doctoral dissertation, Wayne State Univ., Detroit, Mich., 1978.
  • [12] -, Internal characterizations of contractibility for fans, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 27 (1979), 391-395. MR 557408 (81g:54039b)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 54F20, 54F25

Retrieve articles in all journals with MSC: 54F20, 54F25


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1980-0574786-1
Article copyright: © Copyright 1980 American Mathematical Society

American Mathematical Society