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The fundamental group of the orbit space of a discontinuous group

Published online by Cambridge University Press:  24 October 2008

M. A. Armstrong
M. A. Armstrong
Affiliation:
University of Chicago
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Extract

A group G of homeomorphisms of a topological space X will be called discontinuous if

(1) the stabilizer of each point of X is finite, and

(2) each point x ∈ X; has a neighbourhood U such that any element of G not in the stabilizer of x maps U outside itself (i.e. if gx ≠ x then U ∩ gU is empty). The purpose of this note is to prove the following result.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 2 , April 1968 , pp. 299 - 301
Copyright
Copyright © Cambridge Philosophical Society 1968

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References

REFERENCES

(1)Armstrong, M. A.On the fundamental group of an orbit space. Proc. Cambridge Philos. Soc. 61 (1965), 639–646.CrossRefGoogle Scholar
(2)Floyd, E. E.Some characterizations of interior maps. Ann. of Math. 51 (1950), 571–575.CrossRefGoogle Scholar
(3)Hu, S. T.Homotopy Theory (Academic Press, 1959).Google Scholar
(4)Kelley, J. L.General Topology (Van Nostrand, 1955).Google Scholar
(5)Rhodes, F.On the fundamental group of a transformation group. Proc. London Math. Soc. (3) 16 (1966), 635–650.Google Scholar