Geodesic
Discontinuity Conditions on Transformation Groups
Canadian mathematical bulletin, Tome 15 (1972) no. 3, pp. 417-419

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

Throughout this paper, (X, T, π) is a topological transformation group [1], L={x∊X:xt=x for some t∊{e}} and 0=X—L is nonempty; standard topological concepts are used as defined in [2].The problem to be considered here has been studied in [3] and [6]. In [3], X is assumed to be a compact metric space, and each t e T satisfies a convergence condition on certain subsets of X. Under these conditions, Kaul proved that if T is equicontinuous on 0, then the group properties of discontinuity, proper discontinuity, and Sperner's condition (see Definition 1) are equivalent. 
Thompson, D. V. Discontinuity Conditions on Transformation Groups. Canadian mathematical bulletin, Tome 15 (1972) no. 3, pp. 417-419. doi: 10.4153/CMB-1972-075-3
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[1] 1. Gottschalk, W. H. and Hedlund, G. A., Topological Dynamics, Colloq. Publ., Amer. Math. Soc, 1955. Google Scholar

[2] 2. Kelley, J. L., General topology, Van Nostrand, Princeton, N.J., 1955. Google Scholar

[3] 3. Kaul, S. K., On a transformation group, Canad. J. Math. 21 (1969), 935-941. Google Scholar

[4] 4. Kaul, S. K., Compact subsets in function spaces, Canad. Math. Bull. 12 (1969), 461-466. Google Scholar

[5] 5. Kaul, S. K., On the irregular sets of a transformation group, (to appear). Google Scholar

[6] 6. Kinoshita, S., Notes on discontinuous transformation groups, (unpublished). Google Scholar

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