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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
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(5)Rhodes, F.On the fundamental group of a transformation group. Proc. London Math. Soc. (3) 16 (1966), 635–650.Google Scholar