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On the Projective Cover of an orbit space

Part of: Connections with other structures, applications

Published online by Cambridge University Press:  09 April 2009

K. K. Azad  and
Gunjan Agrawal
K. K. Azad
Affiliation:
‘Vijaya Niwas’ 198, Mumfordganj Allahabad, 211002, India
Gunjan Agrawal
Affiliation:
Department of Mathematics and Statistics, University of Allahabad, Allahabad, India
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Abstract

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In this paper, we obtain the projective cover of the orbit space X/G in terms of the orbit space of the projective space of X, when X is a Tychonoff G-space and G is a finite discrete group. An example shows that finiteness of G is needed.

Keywords

Stone spaceStone-Čech compactificationprojective coverorbit space.

MSC classification

Secondary: 54H15: Transformation groups and semigroups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 46 , Issue 2 , April 1989 , pp. 308 - 312
Copyright
Copyright © Australian Mathematical Society 1989

References

Banaschewski, B. (1968), ‘Projective covers in categories of topological spaces and topological algebras’, General topology and its relations to modern analysis and algebra, III, pp. 63–91 (Proc. Conf. Kanpur).Google Scholar
Bredon, G. E. (1972), Introduction to compact transformation groups, (Academic Press, New York).Google Scholar
Gleason, A. M. (1958), ‘Projective topological spaces’, Illinois J. Math. 2, 482–489.CrossRefGoogle Scholar
Hager, A. W. (1971), ‘The projective resolution of a compact space’, Proc. Amer. Math. Soc. 28, 262–266.CrossRefGoogle Scholar
Rainwater, J. (1959), ‘A note on projective resolutions’, Proc. Amer. Math. Soc. 10, 734–735.CrossRefGoogle Scholar
Srivastava, Kavita (1987), ‘On the Stone-Čech compactification of an orbit space’, Bull. Austral. Math. Soc. 36, 435–439.CrossRefGoogle Scholar
Strauss, D. P. (1967), ‘Extremally disconnected spaces’, Proc. Amer. Math. Soc. 18, 305–309.CrossRefGoogle Scholar
Walker, R. C. (1974), The Stone-Čech compactification, (Springer-Verlag, Berlin).CrossRefGoogle Scholar
Willard, S. (1970), General topology, (Addison-Wesley, Reading, Mass.).Google Scholar