%0 Journal Article
%T New Kinds of Transitivity Maps and Minimality Mappings
%A Mohammed Nokhas Murad
%A Omeed Adwal Ali Ali
%J Open Access Library Journal
%V 13
%N 5
%P 1-6
%@ 2333-9721
%D 2026
%I Open Access Library
%R 10.4236/oalib.1113357
%X In this article, we have discussed the connection between two distinct types of map concepts, specifically topological ¦Á-transitive maps [1]-[3] and ¦Ä-transitive maps and explored certain characteristics within two constructed topological spaces from the original space (<em>X</em>,r), denoted by (<em>X</em>,r<sup>a</sup>) and (<em>X</em>,r<sup>s</sup>). Here, Ra represents the ¦Á-topology and r<em><sup>¦Ä</sup></em> represents the ¦Ä-topology of the specified topological space (<em>X</em>,r). These two concepts are delineated by employing ¦Á-irresolute and ¦Ä-irresolute maps, respectively. Additionally, we have examined the correlation between two categories of minimal systems: ¦Á-minimal and ¦Ä-minimal systems. The principal findings are summarized in the ensuing propositions: 1) Every alpha-transitive map implies a delta-transitive map; however, the opposite may not always be the case. 2) Every alpha-minimal system implies a delta-minimal system; however, the opposite may not always be the case.
%K Alpha-Transitive Maps
%K Delta-Minimal System
%K Alpha-Irresolute Maps
%U http://www.oalib.com/paper/6857951