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)

 
 

 

Spaces with given homeomorphism groups


Author: M. C. Thornton
Journal: Proc. Amer. Math. Soc. 33 (1972), 127-131
MSC: Primary 57E05
DOI: https://doi.org/10.1090/S0002-9939-1972-0292054-3
MathSciNet review: 0292054
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A topological space X is constructed so that its group of homeomorphisms is isomorphic to a given finitely generated group G. If G has r generators and finite order n, X has $ n(2r + 1)$ points. The relation of X to certain covering spaces is considered.


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

  • [1] G. Birkhoff, On groups of automorphisms, Rev. Un. Mat. Argentina 11 (1946), 155-157. (Spanish) MR 7, 411. MR 0015387 (7:411a)
  • [2] R. Frucht, Herstellung von Graphen mit vorgegebener abstrakter Gruppe, Compositio Math. 6 (1938), 239-250. MR 1557026
  • [3] R. Frucht, Graphs of degree three with a given abstract group, Canad. J. Math. 1 (1949), 365-378. MR 11, 377. MR 0032987 (11:377c)
  • [4] J. de Groot, Groups represented by homeomorphism groups. I, Math. Ann. 138 (1959), 80-102. MR 22 #9959. MR 0119193 (22:9959)
  • [5] F. Harary, Graph theory, Addison-Wesley, Reading, Mass., 1969. MR 41 #1566. MR 0256911 (41:1566)
  • [6] M. C. McCord, Singular homology groups and homotopy groups of finite topological spaces, Duke Math. J. 33 (1966), 465-474. MR 33 #4930. MR 0196744 (33:4930)
  • [7] R. E. Stong, Finite topological spaces, Trans. Amer. Math. Soc. 123 (1966), 325-340. MR 33 #3247. MR 0195042 (33:3247)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57E05

Retrieve articles in all journals with MSC: 57E05


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0292054-3
Keywords: Finite topological space, A-space, homeomorphism groups, transformation groups, covering spaces, covering transformations
Article copyright: © Copyright 1972 American Mathematical Society

American Mathematical Society