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On the Irregular Sets of a Transformation Group

Published online by Cambridge University Press:  20 November 2018

S. K. Kaul
S. K. Kaul*
Affiliation:
University of Saskatchewan, Regina Saskatchewan
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We assume throughout that (X, T, π) is a transformation group [2], where X is a topological space which is always assumed to be regular and Hausdorff. We call a point x ∊ X regular under T if for any open set U in X and any subset G of T such that , there exists an open set V containing x, such that VG ⊆ U [7]. Let R(X) denote the interior of the set of all the regular points of X under T, and I(X) the set of irregular points of X under T, that is the set of points which are not regular under T.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 2 , June 1973 , pp. 225 - 232
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Dugundji, J., Topology, Allyn and Bacon, Boston, Mass., 1968.Google Scholar
2. Gottschalk, W. H. and Hedlund, G.A., Topological dynamics, Colloq. Publ., American Math. Soc, Providence, R.I., 1955.Google Scholar
3. Gray, W. J. and Roberson, F.A., On the near equicontinuity of transformation groups, Proc. Amer. Math. Soc. 23 (1969), 59–63.Google Scholar
4. Homma, T. and Kinoshita, S., On homeomorphisms which are regular except for a finite number of points, Osaka J. Math. 7 (1955), 29–38.Google Scholar
5. Kaul, S. K., On almost regular homeomorphisms, Canad. J. Math. 20 (1968), 1–6.Google Scholar
6. Kaul, S. K., On a transformation group, Canad. J. Math. 21 (1969), 935–941.Google Scholar
7. Kaul, S. K., Compact subsets in function spaces, Canad. Math. Bull. 12 (1969), 461–466.Google Scholar
8. Kelley, J. L., General topology, Van Nostrand, Princeton, N.J., 1955.Google Scholar
9. Roberson, F. A., Some theorems on the structure of near equicontinuous transformation groups, Canad. J. Math. 23 (1971), 421–425.Google Scholar