Geodesic
Actions of a Locally Compact Group with Zero
Canadian journal of mathematics, Tome 23 (1971) no. 3, pp. 413-420

Voir la notice de l'article provenant de la source Cambridge University Press

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 {x ρ} is a net in X, we say limρxρ = ∞ in X if {x ρ } has no subnet which converges in X. 
Hanson, T. H. McH. Actions of a Locally Compact Group with Zero. Canadian journal of mathematics, Tome 23 (1971) no. 3, pp. 413-420. doi: 10.4153/CJM-1971-043-2
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[1] 1. Hanson, T. H. McH., Actions that fiber and vector semigroups, submitted to Trans. Amer. Math. Soc. Google Scholar

[2] 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] 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] 4. Montgomery, D. and Zippin, L., Topological transformation groups (Interscience, New York 1955). Google Scholar

[5] 5. Steenrod, N. E., The topology of fiber bundles (Princeton University Press, Princeton, 1951). Google Scholar

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