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Conceptions of Transitive Maps in Topological Spaces

By M. Nokhas Murad Kaki and Solaf Ali Hussain


The concepts of topological γ-type transitive maps, α-transitive maps, γ-minimal and α-minimal mappings were introduced by Mohammed Nokhas Murad. . In this paper, the relationship between two different notions of transitive maps, namely topological γ-type transitive maps and topological α-type transitive maps has been studied and some of their properties in two topological spaces (X, τγ) and (X, τα), τγ denotes the γ –topology(resp. τα denotes the α–topology) of a given topological space (X, τ ) has been investigated.. Also, we have proved that there exists γ- dense orbit in X, where X is locally γ- compact Hausdorff space and τγ has a countable basis Also, I study the relationship between two types of minimal mappings, namely, γ-minimal mapping and α-minimal mapping, and I will prove that the properties of γ-type transitive, γ-mixing and γ-minimal maps are preserved under γr-conjugac

Topics: Topologically, Minimal, Irresolute, Type Transitive, Dense, Electronic computers. Computer science, QA75.5-76.95, Instruments and machines, QA71-90, Mathematics, QA1-939, Science, Q
Publisher: IJECCE
Year: 2014
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