New Conceptions of Transitivity and Minimal Mappings
Science Research
Volume 2, Issue 1, February 2014, Pages: 1-6
Received: Dec. 13, 2013; Published: Jan. 30, 2014
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Author
Mohammed Nokhas Murad Kaki, Mathematics Department, School of Science, Faculty of Science & Science Education, University of Sulaimani, Kurdistan Region-Iraq
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Abstract
The concepts of topological δ- transitive maps, α-type transitive maps, δ-minimal and α-minimal mappings were introduced by M. Nokhas Murad Kaki. In this paper, the relationship between two different notions of transitive maps, namely topological δ-type transitive mapsandtopological α-type transitive maps has been studied and some of their properties in two topological spaces (X, τδ)and (X, τα), τδ denotes the δ–topology (resp. τα denotes the α–topology) of a given topological space (X, τ) has been investigated.. Also, we have proved that there exists a dense orbit in X, where X is locally compact Hausdorff space and τ has a countable basis. The main results are the following propositions:Every topologically α-type transitive map is a topologically transitive map which implies topologically δ- transitive map, but the converse not necessarily true., and every α-minimal map is a minimal map which implies δ- minimal map in topological spaces, but the converse not necessarily true. Finally, we have proved that a map which is γr- conjugated to γ-transitive (resp. γ-minimal, γ-mixing) map is γ-transitive (resp. γ-minimal, γ-mixing).
Keywords
Topologically δ-Transitive, δ-Irresolute, δ-Type Transitive,δ-Dense, γ-Dense, γ Transitive
To cite this article
Mohammed Nokhas Murad Kaki, New Conceptions of Transitivity and Minimal Mappings, Science Research. Vol. 2, No. 1, 2014, pp. 1-6. doi: 10.11648/j.sr.20140201.11
References
[1]
M. Stone, Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc., 1934, Vol. 41, p374-381
[2]
A. S. Mashhour, M. E. Abd El-Monsef and S. N. El-Deep, On precontinuousand weak precontinuous mappings, Proc.Math. Phys. Soc. Egypt, 1982, Vol. 51, p 47-53.
[3]
N. V. Velicko, H-closed topological spaces. Amer. Math. Soc. Transl. 1968, Vol. 78, p102-118.
[4]
Mohammed Nokhas Murad, New Types of δ-Transitive Maps, International Journal of Engineering & Technology IJET-IJENS Vol:12 No:06, pp.134-136.
[5]
Levine N., Semi open sets and semi continuity in topological spaces. Amer. Math. Monthly.1963, Vol.70, p 36- 41.
[6]
Bhattacharya P., and Lahiri K.B., Semi-generalized closed sets in topology. Indian J. Math. , 1987, Vol. 29, p376-382.
[7]
Rosas E.,Vielina J., Operator- compact and Operator-connected spaces. Scientific Math. 1998, Vol. 2, No. 1, p203-208.
[8]
Kasahara S., Operation-compact spaces. MathematicaJaponica, 1979, Vol. 24, p97-105.
[9]
M. Caldas, S. Jafari and M. M. Kovar, Some properties ofθ-open sets, Divulge. Mat, 12(2)(2004), p 161-169.
[10]
Caldas M., A note on some applications of α-open sets, UMMS, 2003, Vol. 2, p125-130.
[11]
Mohammed Nokhas Murad, Topologically - Transitive Maps and Minimal Systems Gen. Math. Notes, 2012, Vol. 10, No. 2, pp. 43-53 ISSN 2219-7184; Copyright © ICSRS
[12]
Maheshwari N. S., and Thakur S. S., On α-irresolute mappings, Tamkang J. Math, 1980, Vol. 11, p209-214.
[13]
Ogata N., On some classes of nearly open sets, Pacific J. Math, 1965, Vol. 15, p 961-970..
[14]
F.H. Khedr and T. Noiri.On θ-irresolute functions. Indian J. Math., 1986, Vol. 3, No:28, p 211-217.
[15]
M. Nokhas Murad Kaki, Introduction to θ -Type Transitive Maps on Topological spaces.International Journal of Basic & Applied Sciences IJBAS-IJENS 2012, Vol:12, No:06 p 104-108
[16]
Andrijevie D., Some properties of the topology of α-sets,Math. Vesnik, 1994, p 1 -10
[17]
Arenas G. F., Dontchev J. andPuertas L.M.Some covering properties of the α-topology , 1998.
[18]
Caldas M. and Dontchev J., On space with hereditarily compact α-topologies, Acta. Math. Hung, 1999. Vol. 82, p121-129.
[19]
M. Nokhas Murad Kaki,ON SOME NEW γ -TYPE MAPS ON TOPOLOGICAL SPACES,Journal of Mathematical Sciences: Advances and Applications), 2013, Vol. 20 p. 45-60
[20]
M. Nokhas Murad Kaki, Relationship between New Types of Transitive Maps and Minimal Systems International Journal of Electronics Communication and Computer Engineering, 2013, Volume 4, Issue 6, p. 2278–4209
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