On Ordered Hyperspace Topologies in the Setting of Cech Closure Ordered Spaces

İrem Eroğlu; Sevda Sağıroğlu; Erdal Güner

EN

On Ordered Hyperspace Topologies in the Setting of Cech Closure Ordered Spaces

Abstract

In this work, we introduce some possible ordered hyperspace topologies on families of subsets constructed

in the setting of a Cech closure operator.

Keywords

Hyperspace,closure,preorder

References

[1] Mashhour, A.S. and Ghanim, M.H., On closure spaces. Indian J.pure appl. Math. 14(1983), no.6, 680-691.
[2] Peleg, B., Utility functions for partially ordered topological spaces. Econometrica 38 (1970), 93-96.
[3] Andrijevic´, D., Jelic´, M. and Mrševic´, M., Some properties of Hyperspaces of Cˇ ech closure spaces with Vietorislike Topologies. Filomat 24 (2010), 53-61.
[4] Akin, E., The general topology of dynamical systems. Providence: Amer. Math. Soc., 1993.
[5] Burgess, D.C.J. and McCartan, S. D., Order-continuous functions and order-connected spaces. Proc. Camb. Phill. Soc. 68 (1970), 27-31.
[6]Cech, E., Topological spaces. Czechoslovak Acad. of Sciences, Prague, 1966.
[7] Michael, E., Topologies on spaces of subsets. Trans. Amer. Math.Soc. 71 (1951), 152-183.
[8] Beer, G., Topologies on Closed and Closed Convex Sets. Mathematics and its Application, 268, Kluwer Academic Publisher, Dordrecht, 1993.
[9] Gierz, G., HofmannK. H., Keimel, K., Lawson, J.D., Mislove, M.W. and Scott, D.S., Continuous Lattices and Domains. Cambridge University Press, 2003.
[10] Priestly, H. A. and Davey, B. A., Introduction to Lattices and Order. Cambridge University Press, Cambridge, 1990.

[11] Eroglu, I. and Guner, E., Separation axioms in Cˇ ech closure ordered spaces. Commun. Fac. Sci. Univ. Ank. Ser A1 Math. Stat. 65 (2016), no.2, 1-10.
[12] Slapal, J., A digital anologue of the Jordan Curve theorem. Discrete Applied Mathematics 139 (2004), 231-251.
[13] Chandrasekhara Rao, K., Gowri, R. and Swaminathan, V., Cech Closure Space in Structural Configuration of Proteins. Advanced Studies in Biology 1 (2009), no.2, 95-104.
[14] Nachbin, L., Topology and order. Van Nonstrand Mathematical Studies 4, Princeton, N. J., 1965.
[15] Mrševi´c, M. and Andrijevi´c, D., On -connectedness and -closure spaces. Topology and its Application 123 (2002), 157-166.
[16] Mrševi´c, M., Proper and admissible topologies in closure spaces. Indian J. Pure Appl. Math. 36 (2005), 613-627.
[17] Mrševi´c, M. and Jeli´c, M., Selection principles in Hyperspaces with generalized Vietoris topologies. Topology and its Applications 156 (2008), 124-129.
[18] Evren, Ö. and Ok, E.A., On the muti-utility representation of preference relations. Journal of Mathematical Economics 47 (2011), 554-563.
[19] Bade, S., Nash equilibrium in games with incomplete preferences. Economic theory 26 (2005), 309-332.
[20] McCartan, S. D., Separation axioms for topological ordered spaces. Proc. Camb. Phill. Soc. 64 (1968), 965-973.
[21] McCartan, S. D., A quotient ordered spaces. Proc. Camb. Phill. Soc. 64 (1968), 317-322.
[22] McCartan, S. D., Bicontinuous preordered topological spaces. Pasific J. Math. 38 (1971), 523-529.
[23] Choe, T. H. and Park, Y. S., Embedding Ordered topological spaces into topological semilattices. Semigroup Forum 17 (1979), 188-199.
[24] Thron,W. J., What results are Valid on Closure Spaces. Topology Proceedings 6 (1981), 135-158.
[25] Park, Y. S. andW.T. Park, On Ordered Hyperspaces. J. Korean Math. Soc. 19 (1982), no. 1, 11-17.

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

İrem Eroğlu This is me
0000-0002-0327-781X

Sevda Sağıroğlu
0000-0003-3084-0839

Erdal Güner
0000-0003-4749-1321

Publication Date

October 31, 2018

Submission Date

September 19, 2017

Acceptance Date

May 22, 2018

Published in Issue

Year 2018 Volume: 6 Number: 2

IZ

https://izlik.org/JA86SH76AJ

APA

Eroğlu, İ., Sağıroğlu, S., & Güner, E. (2018). On Ordered Hyperspace Topologies in the Setting of Cech Closure Ordered Spaces. Mathematical Sciences and Applications E-Notes, 6(2), 38-45. https://izlik.org/JA86SH76AJ

AMA

1.Eroğlu İ, Sağıroğlu S, Güner E. On Ordered Hyperspace Topologies in the Setting of Cech Closure Ordered Spaces. Math. Sci. Appl. E-Notes. 2018;6(2):38-45. https://izlik.org/JA86SH76AJ

Chicago

Eroğlu, İrem, Sevda Sağıroğlu, and Erdal Güner. 2018. “On Ordered Hyperspace Topologies in the Setting of Cech Closure Ordered Spaces”. Mathematical Sciences and Applications E-Notes 6 (2): 38-45. https://izlik.org/JA86SH76AJ.

EndNote

Eroğlu İ, Sağıroğlu S, Güner E (October 1, 2018) On Ordered Hyperspace Topologies in the Setting of Cech Closure Ordered Spaces. Mathematical Sciences and Applications E-Notes 6 2 38–45.

IEEE

[1]İ. Eroğlu, S. Sağıroğlu, and E. Güner, “On Ordered Hyperspace Topologies in the Setting of Cech Closure Ordered Spaces”, Math. Sci. Appl. E-Notes, vol. 6, no. 2, pp. 38–45, Oct. 2018, [Online]. Available: https://izlik.org/JA86SH76AJ

ISNAD

Eroğlu, İrem - Sağıroğlu, Sevda - Güner, Erdal. “On Ordered Hyperspace Topologies in the Setting of Cech Closure Ordered Spaces”. Mathematical Sciences and Applications E-Notes 6/2 (October 1, 2018): 38-45. https://izlik.org/JA86SH76AJ.

JAMA

1.Eroğlu İ, Sağıroğlu S, Güner E. On Ordered Hyperspace Topologies in the Setting of Cech Closure Ordered Spaces. Math. Sci. Appl. E-Notes. 2018;6:38–45.

MLA

Eroğlu, İrem, et al. “On Ordered Hyperspace Topologies in the Setting of Cech Closure Ordered Spaces”. Mathematical Sciences and Applications E-Notes, vol. 6, no. 2, Oct. 2018, pp. 38-45, https://izlik.org/JA86SH76AJ.

Vancouver

1.İrem Eroğlu, Sevda Sağıroğlu, Erdal Güner. On Ordered Hyperspace Topologies in the Setting of Cech Closure Ordered Spaces. Math. Sci. Appl. E-Notes [Internet]. 2018 Oct. 1;6(2):38-45. Available from: https://izlik.org/JA86SH76AJ