The fundamental groupoid of the quotient of a Hausdorff space by a discontinuous action of a discrete group is the orbit groupoid of the induced action

Subject: 20F34, 20L13, 20L15  Mathematics  Algebraic Topology  Mathematics  Category Theory

References
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12 references, page 1 of 2
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[1] M. A. Armstrong, On the Fundamental Group of an Orbit Space, Proc. Camb. Phil. Soc., 61, (1965), 639646.
[2] A. F. Beardon, 1983, The Geometry of Discrete Groups, volume 91 of Graduate Texts in Mathematics, SpringerVerlag, BerlinHeidelbergNew York.
[3] R. Brown, 1988, Topology: a geometric account of general topology, homotopy types, and the fundamental groupoid, EllisHorwood, Chichester.
[4] R. Brown and G. DaneshNaruie, The Fundamental Groupoid as a Topological Groupoid, Proc. Edinburgh Math. Soc., 19, (1975), 237244.
[5] P. J. Higgins, Algebras with a Scheme of Operators, Math. Nach., 27, (1963), 115132.
[6] P. J. Higgins, 1971, Categories and Groupoids, van Nostrand, New York.
[7] P. J. Higgins and J. Taylor, 1982, The Fundamental Groupoid and Homotopy Crossed Complex of an Orbit Space, in K. H. Kamps et al., ed., Category Theory: Proceedings Gummersbach 1981, volume 962 of Lecture Notes in Math., 115122, SpringerVerlag.
[8] S. Iyanaga and Y. Kawada, eds., 1987, Encyclopaedic Dictionary of Mathematics, MIT Press, Cambridge, Mass. and London, England, third edition, produced by Mathematical Society of Japan; reviewed by K. O. May.
[9] F. Rhodes, On the Fundamental Group of a Transformation Group, Proc. London Math. Soc., 3, (1966), 635650.
[10] F. Rhodes, On Lifting Transformation Groups, Proc. Amer. Math. Soc., 19, (1968), 905908.

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