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Local T2 extended pseudo-quasi-semi metric spaces

Year 2019, Volume: 68 Issue: 2, 2117 - 2127, 01.08.2019
https://doi.org/10.31801/cfsuasmas.497701

Abstract

In this paper, we characterize various local T₂ extended pseudo-quasi-semi metric spaces and investigate the relationships among these various forms. Finally, we give some invariance properties of these local T₂ extended pseudo-quasi-semi metric spaces.

References

  • Adámek, J., Herrlich, H. and Strecker, G.E., Abstract and Concrete Categories, Wiley, New York, 1990.
  • Albert, G.A., A Note on Quasi-Metric Spaces, Bull. Amer. Math. Soc., 47, (1941), 479-482.
  • Baran, M., Separation Properties, Indian J. Pure Appl. Math., 23(5), (1991), 333-341.
  • Baran, M., Generalized Local Separation Properties, Indian J. pure appl., 25(6), (1994), 615-620.
  • Baran, M. and Altindis, H., T₂-Objects in Topological Categories, Acta Math. Hungar., 71, (1996), 41-48.
  • Baran, M., Separation Properties in Topological Categories, Math. Balkanica, 10, (1996), 39-48.
  • Baran, M., Completely Regular Objects and Normal Objects in Topological Categories, Acta Math. Hungar., 80, (1998), 211-224.
  • Baran, M., T₃ and T₄ -Objects in Topological Categories, Indian J.Pure Appl. Math., 29, (1998), 59-69.
  • Baran, M., A notion of compactness in topological categories, Publ. Math. Debrecen, 50, no. 3-4, (1997), 221-234.
  • Baran, M., Kula, M., A note on connectedness, Publ. Math. Debrecen, 68, (2006), 489-501.
  • Baran, M., PreT₂ Objects in Topological Categories, Appl. Categor. Struct., 17, (2009), 591-602.
  • Baran, T. M., Kula, M., Local T₁ Extended Pseudo-Semi Metric Spaces, Mathematical Sciences and Application E-Notes (MSAEN), Volume 5, Issue 1, (2017), 46-56.
  • Baran, T. M., T₀ and T₁ Extended Pseudo-Quasi-Semi Metric Spaces, Ph. D. Dissertation, Erciyes University, (2018), Kayseri, Turkey.
  • Baran, T. M., Kula, M., Local Pre-Hausdorff Extended Pseudo-Quasi-Semi Metric Spaces, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Volume 68, Number 1, (2019), 862-870.
  • Lowen-Colebunders, E., Function Classes of Cauchy Continuous Maps, Marcel Dekker, New York, 1989.
  • Herrlich, H., Topological Functors, Gen. Topology Appl., 4, (1974), 125-142.
  • Kula, M., Separetion Properties at p for the Topological Category of Cauchy Spaces, Acta Math. Hungar., 136, (2012), 1-15.
  • Larrecq, J.G., Non-Hausdorff Topology and Domain Theory, Cambridge University Press, 2013.
  • Lawvere, F.W., Metric Spaces, Generalized Logic, and Closed Categories, Rend. Sem. Mat. Fis. Milano, 43, (1973), 135-166.
  • Lowen, R., Approach Spaces: The Missing Link in the Topology-Uniformity-Metric Triad, Oxford Mathematical Monographs, Oxford University Press., 1997.
  • Lowen, E. and Lowen, R., A Quasitopos Containing CONV and MET as Full Subcategories, Internat. J. Math. and Math. Sci., 11, (1988), 417-438.
  • R. Lowen, Approach Spaces: a Common Supercategory of TOP and MET, Math. Nachr., 141 (1989), 183-226.
  • Nauwelaerts, M., Cartesian Closed Hull for (Quasi-) Metric Spaces, Comment. Math. Univ. Carolinae, 41, (2000), 559-573.
  • Preuss, G., Theory of Topological Structures, An Approach to topological Categories, D. Reidel Publ. Co., Dordrecht, 1988.
  • W.A. Wilson, On Quasi-Metric Spaces, Amer.J. Math., 53, (1931), 675-684.
Year 2019, Volume: 68 Issue: 2, 2117 - 2127, 01.08.2019
https://doi.org/10.31801/cfsuasmas.497701

Abstract

References

  • Adámek, J., Herrlich, H. and Strecker, G.E., Abstract and Concrete Categories, Wiley, New York, 1990.
  • Albert, G.A., A Note on Quasi-Metric Spaces, Bull. Amer. Math. Soc., 47, (1941), 479-482.
  • Baran, M., Separation Properties, Indian J. Pure Appl. Math., 23(5), (1991), 333-341.
  • Baran, M., Generalized Local Separation Properties, Indian J. pure appl., 25(6), (1994), 615-620.
  • Baran, M. and Altindis, H., T₂-Objects in Topological Categories, Acta Math. Hungar., 71, (1996), 41-48.
  • Baran, M., Separation Properties in Topological Categories, Math. Balkanica, 10, (1996), 39-48.
  • Baran, M., Completely Regular Objects and Normal Objects in Topological Categories, Acta Math. Hungar., 80, (1998), 211-224.
  • Baran, M., T₃ and T₄ -Objects in Topological Categories, Indian J.Pure Appl. Math., 29, (1998), 59-69.
  • Baran, M., A notion of compactness in topological categories, Publ. Math. Debrecen, 50, no. 3-4, (1997), 221-234.
  • Baran, M., Kula, M., A note on connectedness, Publ. Math. Debrecen, 68, (2006), 489-501.
  • Baran, M., PreT₂ Objects in Topological Categories, Appl. Categor. Struct., 17, (2009), 591-602.
  • Baran, T. M., Kula, M., Local T₁ Extended Pseudo-Semi Metric Spaces, Mathematical Sciences and Application E-Notes (MSAEN), Volume 5, Issue 1, (2017), 46-56.
  • Baran, T. M., T₀ and T₁ Extended Pseudo-Quasi-Semi Metric Spaces, Ph. D. Dissertation, Erciyes University, (2018), Kayseri, Turkey.
  • Baran, T. M., Kula, M., Local Pre-Hausdorff Extended Pseudo-Quasi-Semi Metric Spaces, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Volume 68, Number 1, (2019), 862-870.
  • Lowen-Colebunders, E., Function Classes of Cauchy Continuous Maps, Marcel Dekker, New York, 1989.
  • Herrlich, H., Topological Functors, Gen. Topology Appl., 4, (1974), 125-142.
  • Kula, M., Separetion Properties at p for the Topological Category of Cauchy Spaces, Acta Math. Hungar., 136, (2012), 1-15.
  • Larrecq, J.G., Non-Hausdorff Topology and Domain Theory, Cambridge University Press, 2013.
  • Lawvere, F.W., Metric Spaces, Generalized Logic, and Closed Categories, Rend. Sem. Mat. Fis. Milano, 43, (1973), 135-166.
  • Lowen, R., Approach Spaces: The Missing Link in the Topology-Uniformity-Metric Triad, Oxford Mathematical Monographs, Oxford University Press., 1997.
  • Lowen, E. and Lowen, R., A Quasitopos Containing CONV and MET as Full Subcategories, Internat. J. Math. and Math. Sci., 11, (1988), 417-438.
  • R. Lowen, Approach Spaces: a Common Supercategory of TOP and MET, Math. Nachr., 141 (1989), 183-226.
  • Nauwelaerts, M., Cartesian Closed Hull for (Quasi-) Metric Spaces, Comment. Math. Univ. Carolinae, 41, (2000), 559-573.
  • Preuss, G., Theory of Topological Structures, An Approach to topological Categories, D. Reidel Publ. Co., Dordrecht, 1988.
  • W.A. Wilson, On Quasi-Metric Spaces, Amer.J. Math., 53, (1931), 675-684.
There are 25 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Review Articles
Authors

Tesnim Baran 0000-0001-6639-8654

Publication Date August 1, 2019
Submission Date December 15, 2018
Acceptance Date March 27, 2019
Published in Issue Year 2019 Volume: 68 Issue: 2

Cite

APA Baran, T. (2019). Local T2 extended pseudo-quasi-semi metric spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), 2117-2127. https://doi.org/10.31801/cfsuasmas.497701
AMA Baran T. Local T2 extended pseudo-quasi-semi metric spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2019;68(2):2117-2127. doi:10.31801/cfsuasmas.497701
Chicago Baran, Tesnim. “Local T2 Extended Pseudo-Quasi-Semi Metric Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 2 (August 2019): 2117-27. https://doi.org/10.31801/cfsuasmas.497701.
EndNote Baran T (August 1, 2019) Local T2 extended pseudo-quasi-semi metric spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 2 2117–2127.
IEEE T. Baran, “Local T2 extended pseudo-quasi-semi metric spaces”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 2, pp. 2117–2127, 2019, doi: 10.31801/cfsuasmas.497701.
ISNAD Baran, Tesnim. “Local T2 Extended Pseudo-Quasi-Semi Metric Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/2 (August 2019), 2117-2127. https://doi.org/10.31801/cfsuasmas.497701.
JAMA Baran T. Local T2 extended pseudo-quasi-semi metric spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:2117–2127.
MLA Baran, Tesnim. “Local T2 Extended Pseudo-Quasi-Semi Metric Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 2, 2019, pp. 2117-2, doi:10.31801/cfsuasmas.497701.
Vancouver Baran T. Local T2 extended pseudo-quasi-semi metric spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(2):2117-2.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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