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

Year 2018, Volume: 6 Issue: 2, 38 - 45, 31.10.2018

Abstract

In this work, we introduce some possible ordered hyperspace topologies on families of subsets constructed
in the setting of a Cech closure operator.

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.
Year 2018, Volume: 6 Issue: 2, 38 - 45, 31.10.2018

Abstract

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.
There are 25 citations in total.

Details

Primary Language English
Journal Section Articles
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 Issue: 2

Cite

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.
AMA Eroğlu İ, Sağıroğlu S, Güner E. On Ordered Hyperspace Topologies in the Setting of Cech Closure Ordered Spaces. Math. Sci. Appl. E-Notes. October 2018;6(2):38-45.
Chicago Eroğlu, İrem, Sevda Sağıroğlu, and Erdal Güner. “On Ordered Hyperspace Topologies in the Setting of Cech Closure Ordered Spaces”. Mathematical Sciences and Applications E-Notes 6, no. 2 (October 2018): 38-45.
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 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, 2018.
ISNAD Eroğlu, İrem et al. “On Ordered Hyperspace Topologies in the Setting of Cech Closure Ordered Spaces”. Mathematical Sciences and Applications E-Notes 6/2 (October 2018), 38-45.
JAMA 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, 2018, pp. 38-45.
Vancouver 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.

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