TITLE:
New Kinds of Transitivity Maps and Minimality Mappings
AUTHORS:
Mohammed Nokhas Murad, Omeed Adwal Ali Ali
KEYWORDS:
Alpha-Transitive Maps, Delta-Minimal System, Alpha-Irresolute Maps
JOURNAL NAME:
Open Access Library Journal,
Vol.13 No.5,
May
22,
2026
ABSTRACT: In this article, we have discussed the connection between two distinct types of map concepts, specifically topological α-transitive maps [1]-[3] and δ-transitive maps and explored certain characteristics within two constructed topological spaces from the original space
(
X,τ
)
, denoted by
(
X,
τ
α
)
and
(
X,
τ
δ
)
. Here,
τ
α
represents the α-topology and
τ
δ
represents the δ-topology of the specified topological space
(
X,τ
)
. These two concepts are delineated by employing α-irresolute and δ-irresolute maps, respectively. Additionally, we have examined the correlation between two categories of minimal systems: α-minimal and δ-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.