Research Article
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Year 2016, , 6 - 14, 15.04.2016
https://doi.org/10.36753/mathenot.421346

Abstract

References

  • [1] Adámek, J., Herrlich, H. and Strecker, G. E., Abstract and Concrete Categories. Wiley, New York, 1990.
  • [2] Baran, M., Separation properties. Indian J. Pure Appl. Math. 23 (1992), 333-341.
  • [3] Baran, M., Separation Properties at p for the topological categories of reflexive relation spaces and preordered spaces. Math. Balkanica 3 (1992), 193-198.
  • [4] Baran, M., The notion of closedness in topological categories. Comment. Math. Univ. Carolinae 34 (1993), 383-395.
  • [5] Baran, M., Generalized local separation properties. Indian J. Pure Appl. Math. 25 (1994), 615-620.
  • [6] Baran, M., Separation properties in topological categories. Math. Balkanica 10 (1996), 39-48.
  • [7] Baran, M., Completely regular objects and normal objects in topological categories. Acta Math. Hungar. 80 (1998), no. 3, 211-224.
  • [8] Baran, M., T3 and T4-objects in topological categories. Indian J. Pure Appl. Math. 29 (1998), 59-69.
  • [9] Baran, M., Closure operators in convergence spaces. Acta Math.Hungar. 87 (2000), 33-45.
  • [10] Baran, M., Compactness, perfectness, separation, minimality and closedness with respect to closure operators. Applied Categorical Structures 10 (2002), 403-415.
  • [11] Baran, M., PreT 2-objects in topological categories. Applied Categorical Structures 17 (2009), 591-602.
  • [12] Baran, M. and Al-Safar, J., Quotient-reflective and bireflective subcategories of the category of preordered sets. Topology and its Appl. 158 (2011), 2076-2084.
  • [13] Baran, M. and Altındi¸s, H., T0-Objects in topological categories. J. Univ. Kuwait (sci.) 22 (1995), 123-127.
  • [14] Baran, M. and Altındi¸s, H., T2-objects in topological categories. Acta Math. Hungar. 71 (1996), no. 1-2, 41-48.
  • [15] Dikranjan, D. and Giuli, E., Closure operators I. Topology Appl. 27 (1987), 129-143.
  • [16] Johnstone, P. T., Topos Theory. London Math. Soc. Monographs, No.10 Academic Press, New York, 1977.
  • [17] Katetov, M., On continuity structures and spaces of mappings. Comm. Math. Univ. Car. 6 (1965), 257-278.
  • [18] Keller, H., Die limes-uniformisierbarkeit der limesräume. Math. Ann. 176 (1968), 334-341.
  • [19] Kowalsky, H. J., Limesräume und komplettierung. Math. Nachr. 12 (1954), 301-340.
  • [20] Kula, M., A note on Cauchy spaces. Acta Math. Hungar. 133 (2011), no. 1-2, 14-32.
  • [21] Kula, M., Separation properties at p for the topological category of Cauchy Spaces. Acta Math. Hungar. 136 (2012), no. 1-2, 1-15.
  • [22] Lowen-Colebunders, E., Function classes of Cauchy Continuous maps. M. Dekker, New York, 1989.
  • [23] Marny, Th., Rechts-Bikategoriestrukturen in Topologischen Kategorien. Dissertation, Freie Universität Berlin, 1973.
  • [24] Mielke, M. V., Separation axioms and geometric realizations. Indian J. Pure Appl. Math. 25 (1994), 711-722.
  • [25] Nel, L. D., Initially structured categories and cartesian closedness. Canad. Journal of Math. XXVII (1975), 1361- 1377.
  • [26] Preuss, G., Theory of Topological Structures. An Approach to Topological Categories. D. Reidel Publ. Co., Dordrecht, 1988.
  • [27] Preuss, G., Improvement of Cauchy spaces. Q&A in General Topology 9 (1991), 159-166.
  • [28] Preuss, G., Semiuniform convergence spaces. Math. Japon. 41 (1995), 465-491.
  • [29] Rath, N., Precauchy spaces. PH.D. Thesis, Washington State University, 1994.
  • [30] Rath, N., Completion of a Cauchy space without the T2-restriction on the space. Int. J. Math. Math. Sci. 3, 24 (2000), 163-172.
  • [31] Weck-Schwarz, S., T0-objects and separated objects in topological categories. Quaestiones Math. 14 (1991), 315-325.

T3 and T4-Objects at p in the Category of Cauchy Spaces

Year 2016, , 6 - 14, 15.04.2016
https://doi.org/10.36753/mathenot.421346

Abstract

There are various generalization of the usual topological T3 and T4- axioms to topological categories

defined in [2] and [8]. [8] is shown that they lead to different T3 and T4 concepts, in general. In this

paper, an explicit characterizations of each of the separation properties T3 and T4 at a point p and the

generalized separation properties is given in the topological category of Cauchy spaces. Moreover,

specific relationships that arise among the various Ti, i = 0; 1; 2; 3; 4, PreT2; and T2 structures at p and the

generalized separation properties are examined in this category. Finally, we investigate the relationships

between the generalized separation properties and the separation properties at a point p in this category.

References

  • [1] Adámek, J., Herrlich, H. and Strecker, G. E., Abstract and Concrete Categories. Wiley, New York, 1990.
  • [2] Baran, M., Separation properties. Indian J. Pure Appl. Math. 23 (1992), 333-341.
  • [3] Baran, M., Separation Properties at p for the topological categories of reflexive relation spaces and preordered spaces. Math. Balkanica 3 (1992), 193-198.
  • [4] Baran, M., The notion of closedness in topological categories. Comment. Math. Univ. Carolinae 34 (1993), 383-395.
  • [5] Baran, M., Generalized local separation properties. Indian J. Pure Appl. Math. 25 (1994), 615-620.
  • [6] Baran, M., Separation properties in topological categories. Math. Balkanica 10 (1996), 39-48.
  • [7] Baran, M., Completely regular objects and normal objects in topological categories. Acta Math. Hungar. 80 (1998), no. 3, 211-224.
  • [8] Baran, M., T3 and T4-objects in topological categories. Indian J. Pure Appl. Math. 29 (1998), 59-69.
  • [9] Baran, M., Closure operators in convergence spaces. Acta Math.Hungar. 87 (2000), 33-45.
  • [10] Baran, M., Compactness, perfectness, separation, minimality and closedness with respect to closure operators. Applied Categorical Structures 10 (2002), 403-415.
  • [11] Baran, M., PreT 2-objects in topological categories. Applied Categorical Structures 17 (2009), 591-602.
  • [12] Baran, M. and Al-Safar, J., Quotient-reflective and bireflective subcategories of the category of preordered sets. Topology and its Appl. 158 (2011), 2076-2084.
  • [13] Baran, M. and Altındi¸s, H., T0-Objects in topological categories. J. Univ. Kuwait (sci.) 22 (1995), 123-127.
  • [14] Baran, M. and Altındi¸s, H., T2-objects in topological categories. Acta Math. Hungar. 71 (1996), no. 1-2, 41-48.
  • [15] Dikranjan, D. and Giuli, E., Closure operators I. Topology Appl. 27 (1987), 129-143.
  • [16] Johnstone, P. T., Topos Theory. London Math. Soc. Monographs, No.10 Academic Press, New York, 1977.
  • [17] Katetov, M., On continuity structures and spaces of mappings. Comm. Math. Univ. Car. 6 (1965), 257-278.
  • [18] Keller, H., Die limes-uniformisierbarkeit der limesräume. Math. Ann. 176 (1968), 334-341.
  • [19] Kowalsky, H. J., Limesräume und komplettierung. Math. Nachr. 12 (1954), 301-340.
  • [20] Kula, M., A note on Cauchy spaces. Acta Math. Hungar. 133 (2011), no. 1-2, 14-32.
  • [21] Kula, M., Separation properties at p for the topological category of Cauchy Spaces. Acta Math. Hungar. 136 (2012), no. 1-2, 1-15.
  • [22] Lowen-Colebunders, E., Function classes of Cauchy Continuous maps. M. Dekker, New York, 1989.
  • [23] Marny, Th., Rechts-Bikategoriestrukturen in Topologischen Kategorien. Dissertation, Freie Universität Berlin, 1973.
  • [24] Mielke, M. V., Separation axioms and geometric realizations. Indian J. Pure Appl. Math. 25 (1994), 711-722.
  • [25] Nel, L. D., Initially structured categories and cartesian closedness. Canad. Journal of Math. XXVII (1975), 1361- 1377.
  • [26] Preuss, G., Theory of Topological Structures. An Approach to Topological Categories. D. Reidel Publ. Co., Dordrecht, 1988.
  • [27] Preuss, G., Improvement of Cauchy spaces. Q&A in General Topology 9 (1991), 159-166.
  • [28] Preuss, G., Semiuniform convergence spaces. Math. Japon. 41 (1995), 465-491.
  • [29] Rath, N., Precauchy spaces. PH.D. Thesis, Washington State University, 1994.
  • [30] Rath, N., Completion of a Cauchy space without the T2-restriction on the space. Int. J. Math. Math. Sci. 3, 24 (2000), 163-172.
  • [31] Weck-Schwarz, S., T0-objects and separated objects in topological categories. Quaestiones Math. 14 (1991), 315-325.
There are 31 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Muammer Kula

Publication Date April 15, 2016
Submission Date January 17, 2016
Published in Issue Year 2016

Cite

APA Kula, M. (2016). T3 and T4-Objects at p in the Category of Cauchy Spaces. Mathematical Sciences and Applications E-Notes, 4(1), 6-14. https://doi.org/10.36753/mathenot.421346
AMA Kula M. T3 and T4-Objects at p in the Category of Cauchy Spaces. Math. Sci. Appl. E-Notes. April 2016;4(1):6-14. doi:10.36753/mathenot.421346
Chicago Kula, Muammer. “T3 and T4-Objects at P in the Category of Cauchy Spaces”. Mathematical Sciences and Applications E-Notes 4, no. 1 (April 2016): 6-14. https://doi.org/10.36753/mathenot.421346.
EndNote Kula M (April 1, 2016) T3 and T4-Objects at p in the Category of Cauchy Spaces. Mathematical Sciences and Applications E-Notes 4 1 6–14.
IEEE M. Kula, “T3 and T4-Objects at p in the Category of Cauchy Spaces”, Math. Sci. Appl. E-Notes, vol. 4, no. 1, pp. 6–14, 2016, doi: 10.36753/mathenot.421346.
ISNAD Kula, Muammer. “T3 and T4-Objects at P in the Category of Cauchy Spaces”. Mathematical Sciences and Applications E-Notes 4/1 (April 2016), 6-14. https://doi.org/10.36753/mathenot.421346.
JAMA Kula M. T3 and T4-Objects at p in the Category of Cauchy Spaces. Math. Sci. Appl. E-Notes. 2016;4:6–14.
MLA Kula, Muammer. “T3 and T4-Objects at P in the Category of Cauchy Spaces”. Mathematical Sciences and Applications E-Notes, vol. 4, no. 1, 2016, pp. 6-14, doi:10.36753/mathenot.421346.
Vancouver Kula M. T3 and T4-Objects at p in the Category of Cauchy Spaces. Math. Sci. Appl. E-Notes. 2016;4(1):6-14.

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