Minimal sets and stability For Compact sets of I(X)-spaces
DOI:
https://doi.org/10.31642/JoKMC/2018/010306Abstract
The set of all isometries on a metric space X with the usual composition of functions form a group and it is called the group of isometries and is denoted by I(X). In this paper we study the generalization of the concepts of minimal sets, stability and attraction, from dynamic system into the topological transformation group (I(X),X).We find that the collection of all minimal sets of I(X)-space is the collection of all the closures of orbits of X and we found some useful results about stability and attraction and we fixed the relationship among it's kinds.Downloads
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Abdullah, H. K., & Al-Attar, A. I., Some topological properties of I(X)-spaces, AlMustansiriyah, Journal of Science, 21(2010) 441-456.
AL-SRRAAI, S. J., On strongly proper actions, M.sc. Thesis, College of Science , University of AL-Mustansiryah , 2000.
BHATIA, N.P., & G.P, SZEGO, Stability theory of dynamical system, Springer-verlag New York –Heidelberg .Berlin 1970.
BREDON, G.E, introduction to compact transformation groups, Academic press, N, Y, 1972.
DYDO, W, Proper G-spaces, J.Diff. Geometry, 9(1974) 565-569. DOI: https://doi.org/10.4310/jdg/1214432554
GOHSCHALK, W.H, HELUND, G.A., Topological Dynamics, Ammer. Math, Soc, vol.36 providence 1955.
KELLEY, J.L, General topology, Van. Nostrand, Princeton, 1955.
MANOUSSOS, A., STRANZALOS, P, On the groups of isometrics on a locally compact metric space, Journal of lie Theory, 13(2003) 7-12.
MANOUSSOS, A, STRANZALOS, P, The role of connectedness in the structure and the action of group of isometrics of locally compact metric space, arXive: math.GN/0010083 v19
Oct, .2000.
SIBIRSKY, K.S., Introduction to topological dynamics. Noordhoff International Publishing Leydewn,1975 . DOI: https://doi.org/10.1007/978-94-010-2308-5
WILLARD, S., general topology, Addeson-Wesley publishing company, Inc, 1970.
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Copyright (c) 2015 Habeeb Kareem Abdullah, Amal Ibrahim Al-Attar
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