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).
| Published in | Science Research (Volume 2, Issue 1) |
| DOI | 10.11648/j.sr.20140201.11 |
| Page(s) | 1-6 |
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Topologically δ-Transitive, δ-Irresolute, δ-Type Transitive,δ-Dense, γ-Dense, γ Transitive
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APA Style
Mohammed Nokhas Murad Kaki. (2014). New Conceptions of Transitivity and Minimal Mappings. Science Research, 2(1), 1-6. https://doi.org/10.11648/j.sr.20140201.11
ACS Style
Mohammed Nokhas Murad Kaki. New Conceptions of Transitivity and Minimal Mappings. Sci. Res. 2014, 2(1), 1-6. doi: 10.11648/j.sr.20140201.11
AMA Style
Mohammed Nokhas Murad Kaki. New Conceptions of Transitivity and Minimal Mappings. Sci Res. 2014;2(1):1-6. doi: 10.11648/j.sr.20140201.11
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Download@article{10.11648/j.sr.20140201.11,
author = {Mohammed Nokhas Murad Kaki},
title = {New Conceptions of Transitivity and Minimal Mappings},
journal = {Science Research},
volume = {2},
number = {1},
pages = {1-6},
doi = {10.11648/j.sr.20140201.11},
url = {https://doi.org/10.11648/j.sr.20140201.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sr.20140201.11},
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).},
year = {2014}
}
TY - JOUR T1 - New Conceptions of Transitivity and Minimal Mappings AU - Mohammed Nokhas Murad Kaki Y1 - 2014/01/30 PY - 2014 N1 - https://doi.org/10.11648/j.sr.20140201.11 DO - 10.11648/j.sr.20140201.11 T2 - Science Research JF - Science Research JO - Science Research SP - 1 EP - 6 PB - Science Publishing Group SN - 2329-0927 UR - https://doi.org/10.11648/j.sr.20140201.11 AB - 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). VL - 2 IS - 1 ER -
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