On Ordered Hyperspace Topologies in the Setting of Cech Closure Ordered Spaces
Year 2018,
Volume: 6 Issue: 2, 38 - 45, 31.10.2018
İrem Eroğlu
Sevda Sağıroğlu
,
Erdal Güner
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
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- [2] Peleg, B., Utility functions for partially ordered topological spaces. Econometrica 38 (1970), 93-96.
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Topologies. Filomat 24 (2010), 53-61.
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Domains. Cambridge University Press, 2003.
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1990.
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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
İrem Eroğlu
Sevda Sağıroğlu
,
Erdal Güner
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.