| Title:
|
Interaction between cellularity of Alexandroff spaces and entropy of generalized shift maps (English) |
| Author:
|
Shirazi, Fatemah Ayatollah Zadeh |
| Author:
|
Dolatabad, Sahar Karimzadeh |
| Author:
|
Shamloo, Sara |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
57 |
| Issue:
|
3 |
| Year:
|
2016 |
| Pages:
|
397-410 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the following text for a discrete finite nonempty set $K$ and a self-map $\varphi : X\to X$ we investigate interaction between different entropies of generalized shift $\mathop{\sigma_\varphi:K^X\to K^X}$, ${(x_\alpha)_{\alpha\in X}\mapsto (x_{\varphi(\alpha)})_{\alpha\in X}}$ and cellularities of some Alexandroff topologies on $X$. (English) |
| Keyword:
|
Alexandroff topology |
| Keyword:
|
cellularity |
| Keyword:
|
functional Alexandroff topological space |
| Keyword:
|
infinite anti-orbit number |
| Keyword:
|
infinite orbit number |
| MSC:
|
54C70 |
| idZBL:
|
Zbl 06674889 |
| idMR:
|
MR3554519 |
| DOI:
|
10.14712/1213-7243.2015.174 |
| . |
| Date available:
|
2016-09-22T15:31:34Z |
| Last updated:
|
2018-10-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145843 |
| . |
| Reference:
|
[1] Akhavin M., Shirazi F. Ayatollah Zadeh, Dikranjan D., Giordano Bruno A., Hosseini A.: Algebraic entropy of shift endomorphisms on abelian groups.Quaest. Math. 32 (2009), 529–550. MR 2598205, 10.2989/QM.2009.32.4.3.961 |
| Reference:
|
[2] Shirazi F. Ayatollah Zadeh: Dynamical system associated with an onto map $\lambda:A\to A$.a talk in “International Conference on Topology and its Applications”, July 6-11, 2009, Department of Mathematics, Hacettepe University, Ankara, Turkey. |
| Reference:
|
[3] Shirazi F. Ayatollah Zadeh, Dikranjan D.: Set-theoretical entropy: A tool to compute topological entropy.Proceedings ICTA 2011, Islamabad, Pakistan, July 4-10, 2011, Cambridge Scientific Publishers, 2012, pp. 11–32. |
| Reference:
|
[4] Shirazi F. Ayatollah Zadeh, Golestani N.: Functional Alexandroff spaces.Hacet. J. Math. Stat. 40 (2011), no. 4, 515–522. MR 2884331 |
| Reference:
|
[5] Shirazi F. Ayatollah Zadeh, Golestani N.: More about functional Alexandroff topological spaces.Scientia Magna 6 (2010), no. 4, 64–69. |
| Reference:
|
[6] Shirazi F. Ayatollah Zadeh, Kabir K., Heidari Ardi F.: A note on shift theory.Proceedings of ITES-2007, Math. Pannon. 19 (2008), no. 2, 187–195. MR 2553731 |
| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
