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Actions of a Locally Compact Group with Zero

Published online by Cambridge University Press:  20 November 2018

T. H. McH. Hanson
T. H. McH. Hanson*
Affiliation:
The University of Florida, Gainesville, Florida
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In [2] we find the definition of a locally compact group with zero as a locally compact Hausdorff topological semigroup, S, which contains a non-isolated point, 0, such that G = S – {0} is a group. Hofmann shows in [2] that 0 is indeed a zero for S, G is a locally compact topological group, and the unit, 1, of G is the unit of S. We are to study actions of S and G on spaces, and the reader is referred to [4] for the terminology of actions.

If X is a space (all are assumed Hausdorff) and A ⊂ X, A* denotes the closure of A. If {xρ} is a net in X, we say limρxρ = ∞ in X if {xρ} has no subnet which converges in X.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 23 , Issue 3 , June 1971 , pp. 413 - 420
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Hanson, T. H. McH., Actions that fiber and vector semigroups, submitted to Trans. Amer. Math. Soc.Google Scholar
2. Hofmann, K. H., Locally compact semigroups in which a subgroup with compact complement is dense, Trans. Amer. Math. Soc. 106 (1963), 19–51.Google Scholar
3. Home, J. G., Flows that fiber and some semigroup questions, Abstract 638-20, Notices Amer. Math. Soc. 18 (1966), p. 820.Google Scholar
4. Montgomery, D. and Zippin, L., Topological transformation groups (Interscience, New York 1955).Google Scholar
5. Steenrod, N. E., The topology of fiber bundles (Princeton University Press, Princeton, 1951).Google Scholar