3 citations · 8 across the 17 of their papers we have counts for
21 papers
Compact non-uniformizable Li-Yorke chaotic dynamical systems via an example
Mehrnaz Pourattar, Fatemah Ayatollah Zadeh Shirazi
The main aim of this paper is extending the concept of scambled pair and Li--Yorke chaos to non--uniform compact dynamical systems. We show for finite (compact Alexandroff) topolog…
Closed graph property in Alexandroff spaces
Fatemah Ayatollah Zadeh Shirazi, Sajjad Moradi Chaleshtori
In the following text we show if is an Alexandroff space, then has closed graph if and only if it has constant closed value on each connected component of . Moreo…
Topological Stability and Shadowing in Uniform Transformation Semigroups Modulo an Ideal
F. Ayatollah Zadeh Shirazi, E. Hakimi, A. Hosseini +1
In this paper, we introduce and analyze several key dynamical properties-namely shadowing modulo an ideal, expansivity modulo an ideal, and topological stability modulo an ideal-wi…
Closed graph property and Khalimsky spaces
Mehrnaz Pourattar, Fatemah Ayatollah Zadeh Shirazi, Mohammad Reza Mardanbeigi
In the following text for Khalimsky dimensional space we show self--map has closed graph if and only if there exist integers $…
On adjoint invariant classes of shift operators
F. Ayatollah Zadeh Shirazi, E. Hakimi, A. Hosseini +1
In the following text we compute the adjoint of weighted generalized shift operators over Hilbert spaces. We show for a conjugate invariant subset of , the additive…
Uniformizable functional Alexandroff spaces
Fatemah Ayatollah Zadeh Shirazi, Elahe Hakimi, Arezoo Hosseini +1
In the following text we show that the Alexandroff space is uniformizable if and only if the collection of all smallest neighbourhoods is a partition of . Moreover the Alexa…
On pseudo-codecomposition of a transformation group
Safoura Arzanesh, Fatemah Ayatollah Zadeh Shirazi, Reza Rezavand
In the following text we introduce the concept of pseudo-codecomposition of a transformation group, also we show the collection of all transformation groups pseudo-codecomposable t…
Li-Yorke and Devaney chaotic uniform dynamical systems amongst weighted shifts
Fatemah Ayatollah Zadeh Shirazi, Elaheh Hakimi, Arezoo Hosseini +1
In this paper, for finite discrete field , nonempty set , weight vector and weighted generalized shift $σ_{φ,{\mathfrak w}}:F^…
On proximal relations in transformation semigroups arising from generalized shifts
Fatemah Ayatollah Zadeh Shirazi, Amir Fallahpour, Mohammad Reza Mardanbeigi +1
For a finite discrete topological space with at least two elements, a nonempty set , and a map , with (for…
Possible heights of Alexandroff square transformation groups
Fatemah Ayatollah Zadeh Shirazi, Fatemeh Ebrahimifar, Reza Yaghmaeian +1
In the following text we compute possible heights of (Alexandroff square), (unit square with lexicographic order topology) and $\mathbb U…
On Li--Yorke chaotic transformation groups modulo an ideal
Mehrnaz Pourattar, Fatemah Ayatollah Zadeh Shirazi
In the following text we introduce the notion of chaoticity modulo an ideal in the sense of Li-Yorke in topological transformation semigroups and bring some of its elementary prope…
Set-theoretical entropies of Euler's totient function and other number theoretical special functions
Fatemah Ayatollah Zadeh Shirazi, Reza Yaghmaeian
In the following text we show set--theoretical entropy of Euler's totient function and contravariant set--theoretical entropy of Dedekind psi function are zero. Also contravariant…
Top-designs in the category of Fort spaces
Mehrnaz Pourattar, Fatemah Ayatollah Zadeh Shirazi
In infinite topological Fort space , for nonempty subsets of in the following text we answer to this question "Is there any and Top--design of type …
On generalized shift transformation semigroups
Fatemah Ayatollah Zadeh Shirazi, Fatemeh Ebrahimifar
In the following text we prove that for finite discrete with at least two elements and infinite , the generalized shift transformation semigroup is equi…
Possible heights of graph transformation groups
Fatemah Ayatollah Zadeh Shirazi, Arezoo Hosseini, Zahra Nili Ahmadabadi
In the following text we prove that for all finite there exists a topological graph such that is the collection of all possible h…
Set-theoretical entropies of generalized shifts
Zahra Nili Ahmadabadi, Fatemah Ayatollah Zadeh Shirazi
In the following text for arbitrary with at least two elements, nonempty set and self-map we prove the set-theoretical entropy of generalized shift $σ_φ:X^Γ\to X^…
Indicator sequences and indicator topologies of Fort transformation groups
Fatemah Ayatollah Zadeh Shirazi, Fatemeh Ebrahimifar
In the following text we prove that there exists a Fort transformation group with indicator sequence if and only if , moreover…
On a class between Devaney chaotic and Li-Yorke chaotic generalized shift dynamical systems
Fatemah Ayatollah Zadeh Shirazi, Fatemeh Ebrahimifar, Maryam Hagh Jooyan +1
In the following text, for finite discrete with at least two elements, nonempty countable , and we prove the generalized shift dynamical system is dens…
Distributional chaotic generalized shifts
Zahra Nili Ahmadabadi, Fatemah Ayatollah Zadeh Shirazi
Suppose is a finite discrete space with at least two elements, is a nonempty countable set, and consider self--map . We prove that the generalized shift $σ_φ:X^Γ\t…
Specification properties on uniform spaces
Fatemah Ayatollah Zadeh Shirazi, Zahra Nili Ahmadabadi, Bahman Taherkhani +1
In the following text we introduce specification property (stroboscopical property) for dynamical systems on uniform space. We focus on two classes of dynamical systems: generalize…
Algebraic entropy of shift endomorphisms on abelian groups
Maryam Akhavin, Fatemah Ayatollah Zadeh Shirazi, Dikran Dikranjan +2
For every finite-to-one map and for every abelian group , the generalized shift of the direct sum is the endomorphism defined by $(x_i)_{i\inΓ}\ma…