Actions That Fiber and Vector Semigroups
Canadian journal of mathematics, Tome 24 (1972) no. 1, pp. 29-37
Voir la notice de l'article provenant de la source Cambridge University Press
From [2], we can derive a criterion for determining when an action of a Lie group on a locally compact space leads to a fiber bundle. Here, we present an equivalent criterion which can be stated purely in the language of actions of groups on spaces. This is Theorem I. Using this result, we are able to give a version of a result of Home [1] for dimensions greater than one. This is done in Theorem IV and Corollary IVA. In Theorem II, we show that if a vector semigroup acts on a space X, then whenever the map t ↦ tx is 1 — 1 from onto x, it is in fact a homeomorphism. Also, is a closed subset of X. This is also a version of a result in [1].
Hanson, T. H. McH. Actions That Fiber and Vector Semigroups. Canadian journal of mathematics, Tome 24 (1972) no. 1, pp. 29-37. doi: 10.4153/CJM-1972-004-6
@article{10_4153_CJM_1972_004_6,
author = {Hanson, T. H. McH.},
title = {Actions {That} {Fiber} and {Vector} {Semigroups}},
journal = {Canadian journal of mathematics},
pages = {29--37},
year = {1972},
volume = {24},
number = {1},
doi = {10.4153/CJM-1972-004-6},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1972-004-6/}
}
[1] 1. Home, J. G., Flows that fiber and some semigroup questions, Notices Amer. Math. Soc. 13 (1966), 821. Google Scholar
[2] 2. Paul S., Mostert, Sections in principal fiber spaces, Duke Math. J. 23 (1956), 57–71. Google Scholar
[3] 3. Steenrod, N. E., The topology of fiber bundles (Princeton University Press, Princeton, N.J., 1951). Google Scholar
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