In this paper, we characterize local pre-Hausdorff extended pseudo-quasi-semi metric spaces and investigate the relationships between them. Finally, we show that local pre-Hausdorff extended pseudo-quasi-semi metric spaces are hereditary and productive
Adámek, J., Herrlich, H. and Strecker, G.E., Abstract and Concrete Categories, Wiley, New York, 1990.
Adámek, J. and Reiterman, J., Cartesian Closed Hull for Metric Spaces, Comment. Math. Univ. Carolinae, 31, (1990), 1-6.
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., PreT₂ Objects in Topological Categories, Appl. Categor. Struct., 17, (2009), 591-602.
Baran, M. and Al-Safar, J., Quotient-Reflective and Bireflective Subcategories ot the Category of Preordered Sets, Topology Appl., 158, (2011), 2076-2084.
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.
Johnstone, P.T., Topos Theory, L.M.S Mathematics Monograph: No. 10 Academic Press, New York, 1977.
Kula, M., A Note on Cauchy Spaces, Acta Math. Hungar., 133, (2011), 14-32.
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.
MacLane, S. and Moerdijk, I., Sheaves in Geometry and Logic, Springer- Verlag, 1992.
Mielke, M. V., Separation Axioms and Geometric Realizations, Indian J.Pure Appl. Math., 25, (1994), 711-722.
Mielke, M. V. and Stine, J., Pre-Hausdorff Objects, Publ. Math. Debrecen, 73, (2008), 379-390.
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.
Royden, H. L., Real Analysis, Macmillian Publishing Co., Inc., 1968.
Year 2019,
Volume: 68 Issue: 1, 862 - 870, 01.02.2019
Adámek, J., Herrlich, H. and Strecker, G.E., Abstract and Concrete Categories, Wiley, New York, 1990.
Adámek, J. and Reiterman, J., Cartesian Closed Hull for Metric Spaces, Comment. Math. Univ. Carolinae, 31, (1990), 1-6.
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., PreT₂ Objects in Topological Categories, Appl. Categor. Struct., 17, (2009), 591-602.
Baran, M. and Al-Safar, J., Quotient-Reflective and Bireflective Subcategories ot the Category of Preordered Sets, Topology Appl., 158, (2011), 2076-2084.
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.
Johnstone, P.T., Topos Theory, L.M.S Mathematics Monograph: No. 10 Academic Press, New York, 1977.
Kula, M., A Note on Cauchy Spaces, Acta Math. Hungar., 133, (2011), 14-32.
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.
MacLane, S. and Moerdijk, I., Sheaves in Geometry and Logic, Springer- Verlag, 1992.
Mielke, M. V., Separation Axioms and Geometric Realizations, Indian J.Pure Appl. Math., 25, (1994), 711-722.
Mielke, M. V. and Stine, J., Pre-Hausdorff Objects, Publ. Math. Debrecen, 73, (2008), 379-390.
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.
Royden, H. L., Real Analysis, Macmillian Publishing Co., Inc., 1968.
Baran, T. M., & Kula, M. (2019). Local pre-Hausdorff extended pseudo-quasi-semi metric spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1), 862-870. https://doi.org/10.31801/cfsuasmas.484924
AMA
Baran TM, Kula M. Local pre-Hausdorff extended pseudo-quasi-semi metric spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2019;68(1):862-870. doi:10.31801/cfsuasmas.484924
Chicago
Baran, Tesnim Meryem, and Muammer Kula. “Local Pre-Hausdorff Extended Pseudo-Quasi-Semi Metric Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 1 (February 2019): 862-70. https://doi.org/10.31801/cfsuasmas.484924.
EndNote
Baran TM, Kula M (February 1, 2019) Local pre-Hausdorff extended pseudo-quasi-semi metric spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 1 862–870.
IEEE
T. M. Baran and M. Kula, “Local pre-Hausdorff extended pseudo-quasi-semi metric spaces”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 1, pp. 862–870, 2019, doi: 10.31801/cfsuasmas.484924.
ISNAD
Baran, Tesnim Meryem - Kula, Muammer. “Local Pre-Hausdorff Extended Pseudo-Quasi-Semi Metric Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/1 (February 2019), 862-870. https://doi.org/10.31801/cfsuasmas.484924.
JAMA
Baran TM, Kula M. Local pre-Hausdorff extended pseudo-quasi-semi metric spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:862–870.
MLA
Baran, Tesnim Meryem and Muammer Kula. “Local Pre-Hausdorff Extended Pseudo-Quasi-Semi Metric Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 1, 2019, pp. 862-70, doi:10.31801/cfsuasmas.484924.
Vancouver
Baran TM, Kula M. Local pre-Hausdorff extended pseudo-quasi-semi metric spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(1):862-70.