Interaction between cellularity of Alexandroff spaces and entropy of generalized shift maps

Fatemah Ayatollah Zadeh Shirazi; Sahar Karimzadeh Dolatabad; Sara Shamloo

Commentationes Mathematicae Universitatis Carolinae (2016)

  • Volume: 57, Issue: 3, page 397-410
  • ISSN: 0010-2628

Abstract

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In the following text for a discrete finite nonempty set K and a self-map ϕ : X → X we investigate interaction between different entropies of generalized shift σ ϕ : K X → K X , ( x α ) α ∈ X ↦ ( x ϕ ( α ) ) α ∈ X and cellularities of some Alexandroff topologies on X .

How to cite

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Shirazi, Fatemah Ayatollah Zadeh, Dolatabad, Sahar Karimzadeh, and Shamloo, Sara. "Interaction between cellularity of Alexandroff spaces and entropy of generalized shift maps." Commentationes Mathematicae Universitatis Carolinae 57.3 (2016): 397-410. <http://eudml.org/doc/286785>.

@article{Shirazi2016,
abstract = {In the following text for a discrete finite nonempty set $K$ and a self-map $\varphi : X\rightarrow X$ we investigate interaction between different entropies of generalized shift $\mathop \{\sigma _\varphi :K^X\rightarrow K^X\}$, $\{(x_\alpha )_\{\alpha \in X\}\mapsto (x_\{\varphi (\alpha )\})_\{\alpha \in X\}\}$ and cellularities of some Alexandroff topologies on $X$.},
author = {Shirazi, Fatemah Ayatollah Zadeh, Dolatabad, Sahar Karimzadeh, Shamloo, Sara},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Alexandroff topology; cellularity; functional Alexandroff topological space; infinite anti-orbit number; infinite orbit number},
language = {eng},
number = {3},
pages = {397-410},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Interaction between cellularity of Alexandroff spaces and entropy of generalized shift maps},
url = {http://eudml.org/doc/286785},
volume = {57},
year = {2016},
}

TY - JOUR
AU - Shirazi, Fatemah Ayatollah Zadeh
AU - Dolatabad, Sahar Karimzadeh
AU - Shamloo, Sara
TI - Interaction between cellularity of Alexandroff spaces and entropy of generalized shift maps
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2016
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 57
IS - 3
SP - 397
EP - 410
AB - In the following text for a discrete finite nonempty set $K$ and a self-map $\varphi : X\rightarrow X$ we investigate interaction between different entropies of generalized shift $\mathop {\sigma _\varphi :K^X\rightarrow K^X}$, ${(x_\alpha )_{\alpha \in X}\mapsto (x_{\varphi (\alpha )})_{\alpha \in X}}$ and cellularities of some Alexandroff topologies on $X$.
LA - eng
KW - Alexandroff topology; cellularity; functional Alexandroff topological space; infinite anti-orbit number; infinite orbit number
UR - http://eudml.org/doc/286785
ER -

References

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  2. Shirazi F. Ayatollah Zadeh, Dynamical system associated with an onto map λ : A → A , a talk in “International Conference on Topology and its Applications”, July 6-11, 2009, Department of Mathematics, Hacettepe University, Ankara, Turkey. 
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