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Transformation groups of automorphisms of $ C(X,\,G)$

Author: J. S. Yang
Journal: Proc. Amer. Math. Soc. 39 (1973), 619-624
MSC: Primary 54H15
Erratum: Proc. Amer. Math. Soc. 48 (1975), 517.
MathSciNet review: 0317308
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Abstract: If $ (X,T,\pi )$ is a transformation group with locally compact phase group $ T$, there is a standard way to induce a transformation group on $ C(X,Y)$ endowed with the compact-open topology, where $ Y$ is a uniform space. In this paper, we consider the case where $ Y$ is a topological group $ G$. The reverse construction under certain conditions is also considered.

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

  • [1] J. W. England and L. H. Lanier, Jr., Transformation groups of automorphisms of $ C(X)$, Illinois J. Math 12 (1968), 397-402. MR 37 #1517. MR 0225927 (37:1517)
  • [2] L. Gillman and M. Jerison, Rings of continuous functions, University Series in Higher Math., Van Nostrand, Princeton, N.J., 1960. MR 22 #6994. MR 0116199 (22:6994)
  • [3] W. H. Gottschalk and G. A. Hedlund, Topological dynamics, Amer. Math. Soc. Colloq. Publ., vol. 36, Amer. Math. Soc., Providence, R.I., 1955. MR 17, 650. MR 0074810 (17:650e)
  • [4] E. Hewitt and K. A. Ross, Abstract harmonic analysis. Vol. I: Structure of topological groups. Integration theory, group representations, Die Grundlehren der math. Wissenschaften, Band 115, Academic Press, New York; Springer-Verlag, Berlin, 1963. MR 28 #158. MR 551496 (81k:43001)
  • [5] J. L. Kelley, General topology, Van Nostrand, Princeton, N.J. 1955. MR 16, 1136. MR 0070144 (16:1136c)
  • [6] J. S. Yang, On topological groups and homotopy groups (submitted).

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Keywords: Topological group, transformation group, isomorphism, periodic, recursive, minimal
Article copyright: © Copyright 1973 American Mathematical Society

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