Abstract
In this note we present an attempt at a topological study of a part of the theory of discontinuous groups (see for instance [1]). The idea is to study it as an effective transformation group G on a compact metric space X, where any element of G is a homeomorphism of type 2 (see § 1.1) or the identity of X. Some results are given in § 2, which are more or less like that of discontinuous groups. However the author does not know how to characterize the discontinuity theorem topologically (see for instance [1]). In § 1 we study a special case; and results will be applied in § 2. In § 3 a theorem related to covering transformation groups is proved.
This research was supported in part by NSF Grant GP-5458.
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References
Lehner, J.: Discontinuous groups and automorphic functions, Amer. Math. Soc. (1964).
Kinoshita, S.: On quasi-translations in 3-space, Topology of 3-manifolds, edited by M. K. Fort, Prentice-Hall, Inc. 223–226 (1962).
Homma, T., and S. Kinoshita: On the regularity of homeomorphisms of E n, Jour. Math. Soc. Japan, 5, 365–371 (1953).
Kinoshita, S.: Notes on covering transformation groups, Proc. Amer. Math. Soc. 19, 421–424 (1968).
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Kinoshita, S. (1968). On a Kind of Discrete Transformation Group. In: Mostert, P.S. (eds) Proceedings of the Conference on Transformation Groups. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46141-5_42
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DOI: https://doi.org/10.1007/978-3-642-46141-5_42
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