Equicontinuity and indivisibility in transformation groups
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- by Ping-fun Lam
- Trans. Amer. Math. Soc. 174 (1972), 399-424
- DOI: https://doi.org/10.1090/S0002-9947-1972-0309090-5
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Abstract:
A notion called indivisibility for transformation groups is studied in some detail. The proofs of some theorems announced in [10] are given. Certain types of nonequicontinuous sets which do not disconnect their metric continuum phase spaces and which were not known to exist previously are exhibited.References
- N. Bourbaki, Éléments de mathématique. Part. 1. Les structures fondamentales de l’analyse. Livre III: Topologie générale, Actualités Sci. Indust., no. 1029, Hermann, Paris, 1947; English transl., Addison-Wesley, Reading, Mass., 1966. MR 9, 261; MR 34 #5044b.
- M. K. Fort Jr., The embedding of homeomorphisms in flows, Proc. Amer. Math. Soc. 6 (1955), 960–967. MR 80911, DOI 10.1090/S0002-9939-1955-0080911-2
- W. H. Gottschalk, Minimal sets: an introduction to topological dynamics, Bull. Amer. Math. Soc. 64 (1958), 336–351. MR 100048, DOI 10.1090/S0002-9904-1958-10223-2
- Walter Helbig Gottschalk and Gustav Arnold Hedlund, Topological dynamics, American Mathematical Society Colloquium Publications, Vol. 36, American Mathematical Society, Providence, R.I., 1955. MR 0074810
- William J. Gray and Fred A. Roberson, On the near equicontinuity of transformation groups, Proc. Amer. Math. Soc. 23 (1969), 59–63. MR 246279, DOI 10.1090/S0002-9939-1969-0246279-3
- Tatsuo Homma and Shin’ichi Kinoshita, On homeomorphisms which are regular except for a finite number of points, Osaka Math. J. 7 (1955), 29–38. MR 70159
- S. K. Kaul, On almost regular homeomorphisms, Canadian J. Math. 20 (1968), 1–6. MR 222858, DOI 10.4153/CJM-1968-001-5
- John L. Kelley, General topology, D. Van Nostrand Co., Inc., Toronto-New York-London, 1955. MR 0070144
- K. Kuratowski, Topology. Vol. II, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe [Polish Scientific Publishers], Warsaw, 1968. New edition, revised and augmented; Translated from the French by A. Kirkor. MR 0259835
- Ping-fun Lam, On a theorem of B. Von Kerékjártó, Bull. Amer. Math. Soc. 77 (1971), 230–234. MR 267557, DOI 10.1090/S0002-9904-1971-12695-2
- Ping Fun Lam, Almost equicontinuous transformation groups, Trans. Amer. Math. Soc. 195 (1974), 165–200. MR 377957, DOI 10.1090/S0002-9947-1974-0377957-X
- Nelson G. Markley, Transitive homeomorphisms of the circle, Math. Systems Theory 2 (1968), 247–249. MR 236905, DOI 10.1007/BF01694008
- Waclaw Sierpinski, General topology, Mathematical Expositions, No. 7, University of Toronto Press, Toronto, 1952. Translated by C. Cecilia Krieger. MR 0050870
- Lynn A. Steen and J. Arthur Seebach Jr., Counterexamples in topology, Holt, Rinehart and Winston, Inc., New York-Montreal, Que.-London, 1970. MR 0266131
Bibliographic Information
- © Copyright 1972 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 174 (1972), 399-424
- MSC: Primary 54H20
- DOI: https://doi.org/10.1090/S0002-9947-1972-0309090-5
- MathSciNet review: 0309090