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Year 2019, Volume: 48 Issue: 4, 1079 - 1091, 08.08.2019

Abstract

References

  • [1] D. Andrijević, M. Jelić and M. Mršević, Some properties of Hyperspaces of Čech closure spaces with Vietoris-like Topologies, Filomat, 24 (4), 53–61, 2010.
  • [2] D. Andrijević, M. Jelić and M. Mršević, On function spaces topologies in the setting of Čech closure spaces, Topology Appl. 158, 1390–1395, 2011.
  • [3] D.C.J. Burgess and S.D. McCartan, Order-continuous functions and order-connected spaces, Proc. Camb. Phill. Soc. 68, 27–31, 1970.
  • [4] E. Čech, Topological spaces, Czechoslovak Acad. of Sciences, Prague, 1966.
  • [5] İ Eroğlu and E. Güner, Separation axioms in Čech closure ordered spaces, Commun. Fac. Sci. Univ. Ank. Ser A1 Math. Stat. 65 (2), 1–10, 2016.
  • [6] A.S. Mashhour and M.H. Ghanim, On closure spaces, Indian J. Pure Appl. Math. 14 (6), 680–691, 1983.
  • [7] S.D. McCartan, A quotient ordered spaces, Proc. Camb. Phill. Soc. 64, 317–322, 1968
  • [8] S.D. McCartan, Separation axioms for topological ordered spaces, Proc. Camb. Phill. Soc. 64, 965–973, 1968.
  • [9] S.D. McCartan, Bicontinuous preordered topological spaces, Pasific J. Math. 38, 523– 529, 1971.
  • [10] E. Minguzzi, Normally Preordered Spaces and Utilities, Order, 30, 137–150, 2013.
  • [11] M. Mršević, Proper and admissible topologies in closure spaces, Indian J. Pure Appl. Math. 36, 613–627, 2005.
  • [12] M. Mršević and D. Andrijević, On θ-connectednes and θ-closure spaces, Topology Appl. 123, 157–166, 2002.
  • [13] M. Mršević and M. Jelić, Selection principles in hyperspaces with generalized Vietoris topologies, Topology Appl. 156, 124–129, 2008.
  • [14] L. Nachbin, Topology and order, Van Nonstrand Mathematical Studies 4, Princeton, 1965.
  • [15] K.R. Nailana, Ordered Spaces and Quasi-Uniformities on Spaces of Continuous Order-Preserving Functions, Extracta Math. 15 (3), 513–530, 2000.
  • [16] W. Page, Topological Uniform Structures, Dover Publications Inc. New York, 1989.
  • [17] H.A. Priestly and B.A. Davey, Introduction to Lattices and Order, Cambridge University Press, Cambridge, 1990.
  • [18] C.K. Rao, R. Gowri and V. Swaminathan, Čech Closure Space in Structural Configuration of Proteins, Adv. Stud. in Biol. 1 (2), 95–104, 2009.
  • [19] J. Slapal, A digital anologue of the Jordan Curve theorem, Discrete Appl. Math. 139, 231–251, 2004.
  • [20] J. Williams, Locally Uniform Spaces, Trans. Amer. Math. Soc. 168, 435–469, 1972.

Some ordered function space topologies and ordered semi-uniformizability

Year 2019, Volume: 48 Issue: 4, 1079 - 1091, 08.08.2019

Abstract

In this work, we define some Čech based ordered function space topologies and we introduce ordered semi-uniformizability. Then we investigate ordered semi-uniformizability of the ordered function space topologies such as compact-open (interior) and point-open (interior) ordered topologies.

References

  • [1] D. Andrijević, M. Jelić and M. Mršević, Some properties of Hyperspaces of Čech closure spaces with Vietoris-like Topologies, Filomat, 24 (4), 53–61, 2010.
  • [2] D. Andrijević, M. Jelić and M. Mršević, On function spaces topologies in the setting of Čech closure spaces, Topology Appl. 158, 1390–1395, 2011.
  • [3] D.C.J. Burgess and S.D. McCartan, Order-continuous functions and order-connected spaces, Proc. Camb. Phill. Soc. 68, 27–31, 1970.
  • [4] E. Čech, Topological spaces, Czechoslovak Acad. of Sciences, Prague, 1966.
  • [5] İ Eroğlu and E. Güner, Separation axioms in Čech closure ordered spaces, Commun. Fac. Sci. Univ. Ank. Ser A1 Math. Stat. 65 (2), 1–10, 2016.
  • [6] A.S. Mashhour and M.H. Ghanim, On closure spaces, Indian J. Pure Appl. Math. 14 (6), 680–691, 1983.
  • [7] S.D. McCartan, A quotient ordered spaces, Proc. Camb. Phill. Soc. 64, 317–322, 1968
  • [8] S.D. McCartan, Separation axioms for topological ordered spaces, Proc. Camb. Phill. Soc. 64, 965–973, 1968.
  • [9] S.D. McCartan, Bicontinuous preordered topological spaces, Pasific J. Math. 38, 523– 529, 1971.
  • [10] E. Minguzzi, Normally Preordered Spaces and Utilities, Order, 30, 137–150, 2013.
  • [11] M. Mršević, Proper and admissible topologies in closure spaces, Indian J. Pure Appl. Math. 36, 613–627, 2005.
  • [12] M. Mršević and D. Andrijević, On θ-connectednes and θ-closure spaces, Topology Appl. 123, 157–166, 2002.
  • [13] M. Mršević and M. Jelić, Selection principles in hyperspaces with generalized Vietoris topologies, Topology Appl. 156, 124–129, 2008.
  • [14] L. Nachbin, Topology and order, Van Nonstrand Mathematical Studies 4, Princeton, 1965.
  • [15] K.R. Nailana, Ordered Spaces and Quasi-Uniformities on Spaces of Continuous Order-Preserving Functions, Extracta Math. 15 (3), 513–530, 2000.
  • [16] W. Page, Topological Uniform Structures, Dover Publications Inc. New York, 1989.
  • [17] H.A. Priestly and B.A. Davey, Introduction to Lattices and Order, Cambridge University Press, Cambridge, 1990.
  • [18] C.K. Rao, R. Gowri and V. Swaminathan, Čech Closure Space in Structural Configuration of Proteins, Adv. Stud. in Biol. 1 (2), 95–104, 2009.
  • [19] J. Slapal, A digital anologue of the Jordan Curve theorem, Discrete Appl. Math. 139, 231–251, 2004.
  • [20] J. Williams, Locally Uniform Spaces, Trans. Amer. Math. Soc. 168, 435–469, 1972.
There are 20 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

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

Erdal Güner 0000-0003-4749-1321

Publication Date August 8, 2019
Published in Issue Year 2019 Volume: 48 Issue: 4

Cite

APA Eroğlu, İ., & Güner, E. (2019). Some ordered function space topologies and ordered semi-uniformizability. Hacettepe Journal of Mathematics and Statistics, 48(4), 1079-1091.
AMA Eroğlu İ, Güner E. Some ordered function space topologies and ordered semi-uniformizability. Hacettepe Journal of Mathematics and Statistics. August 2019;48(4):1079-1091.
Chicago Eroğlu, İrem, and Erdal Güner. “Some Ordered Function Space Topologies and Ordered Semi-Uniformizability”. Hacettepe Journal of Mathematics and Statistics 48, no. 4 (August 2019): 1079-91.
EndNote Eroğlu İ, Güner E (August 1, 2019) Some ordered function space topologies and ordered semi-uniformizability. Hacettepe Journal of Mathematics and Statistics 48 4 1079–1091.
IEEE İ. Eroğlu and E. Güner, “Some ordered function space topologies and ordered semi-uniformizability”, Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 4, pp. 1079–1091, 2019.
ISNAD Eroğlu, İrem - Güner, Erdal. “Some Ordered Function Space Topologies and Ordered Semi-Uniformizability”. Hacettepe Journal of Mathematics and Statistics 48/4 (August 2019), 1079-1091.
JAMA Eroğlu İ, Güner E. Some ordered function space topologies and ordered semi-uniformizability. Hacettepe Journal of Mathematics and Statistics. 2019;48:1079–1091.
MLA Eroğlu, İrem and Erdal Güner. “Some Ordered Function Space Topologies and Ordered Semi-Uniformizability”. Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 4, 2019, pp. 1079-91.
Vancouver Eroğlu İ, Güner E. Some ordered function space topologies and ordered semi-uniformizability. Hacettepe Journal of Mathematics and Statistics. 2019;48(4):1079-91.