Equicontinuity and indivisibility in transformation groups

Lam, Ping-fun

doi:10.1090/S0002-9947-1972-0309090-5

Equicontinuity and indivisibility in transformation groups
HTML articles powered by AMS MathViewer

by Ping-fun Lam PDF

Trans. Amer. Math. Soc. 174 (1972), 399-424 Request permission

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

Les structures fondamentales de l’analyse

Topologie générale

9

34

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