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Tychonoff Objects in the Topological Category of Cauchy Spaces

Year 2018, Volume: 6 Issue: 2, 28 - 37, 31.10.2018

Muammer Kula , Sümeyye Kula

https://doi.org/10.36753/mathenot.476787

Abstract

Keywords

Topological category Cauchy space Cauchy map Separation

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., Stacks and filters. Turkish J. of Math.-Do˘ga. 16 (1992), 95-108.
  • [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., A notion of compactness in topological categories. Publ. Math. Debrecen. 50 (3-4), 221-234, 1997.
  • [7] Baran, M., T3 and T4-objects in topological categories. Indian J. Pure Appl. Math. 29 (1), 59-69, 1998.
  • [8] Baran, M., Closure operators in convergence spaces. Acta Math. Hungar. 87 (2000), 33-45.
  • [9] Baran, M., Compactness, perfectness, separation, minimality and closedness with respect to closure operators. Applied Categorical Structures. 10 (2002), 403-415.
  • [10] Baran, M., PreT2-objects in topological categories. Applied Categorical Structures. 17 (2009), 591-602, DOI 10.1007/s10485-008-9161-4.
  • [11] Baran, M. and Altındi¸s, H., T2-objects in topological categories. Acta Math. Hungar. 71 (1996), no. 1-2, 41-48.
  • [12] Baran, M. and Kula, M., A note on separation and compactness in categories of convergence spaces. Proceedings of the International Conference on Applicable General Topology (Ankara, 2001). Appl. Gen. Topol. 4 (1), 1-13, 2003.
  • [13] Bentley, H. L., Herrlich, H. and Lowen-Colebunders, E., Convergence. J. Pure Appl. Algebra. 68 (1990), no 1-2, 27-45.
  • [14] Dikranjan, D. and Giuli, E. Closure operators I. Topology Appl. 27 (1987), 129-143.
  • [15] Johnstone, P.T., Topos Theory. London Math. Soc. Monographs. No. 10, Academic Press, New York, 1977.
  • [16] Katˇetov, M., On continuity structures and spaces of mappings. Comm. Math. Univ. Car. 6 (1965), 257-278.
  • [17] Keller, H., Die Limes-uniformisierbarkeit der Limesräume. Math. Ann. 176 (1968), 334-341.
  • [18] Kent, D. C. and Richardson, G. D., Cauchy Spaces with Regular Completions. Pacific J. Math. 3 (1984), 105-116.
  • [19] Kent, D. C. and Richardson, G. D., Cauchy Completion Categories. Canad. Math. Bull. 32 (1989), 78-83.
  • [20] Kowalsky, H. J., Limesräume und Komplettierung. Math. Nachr. 12 (1954), 301-340.
  • [21] Kula, M., A Note on Cauchy Spaces. Acta Math. Hungar. 133 (2011), no. 1-2, 14-32, DOI:10.1007/s10474-011- 0136-9.
  • [22] Kula, M., Separation properties at p for the topological category of Cauchy Spaces. Acta Math. Hungar. 136 (2012), no. 1-2, 1-15, DOI: 10.1007/s10474-012-0238-z.
  • [23] Kula, M., T3 and T4-Objects in the Topological Category of Cauchy Spaces. Communications, Series A1:Mathematics and Statistics. 66 (2017), no. 1, 29-42.
  • [24] Lowen-Colebunders, E., Function classes of Cauchy Continuous maps M. Dekker, New York, 1989.
  • [25] Marny, Th., Rechts-Bikategoriestrukturen in topologischen Kategorien. Dissertation, Freie Universität Berlin, 1973.
  • [26] Mielke, M.V., Separation axioms and geometric realizations. Indian J. Pure Appl. Math. 25 (1994), 711-722.
  • [27] Munkres, J. R., Topology:A First Course, Prentice-Hall, 1975.
  • [28] Nel, L. D., Initially structured categories and cartesian closedness. Canad. Journal of Math. XXVII (1975), 1361-1377.
  • [29] Preuss, G., Theory of Topological Structures. An Approach to Topological Categories., D. Reidel Publ. Co., Dordrecht, 1988.
  • [30] Preuss, G., Improvement of Cauchy spaces. Q&A in General Topology. 9 (1991), 159-166.
  • [31] Ramaley, J. F. andWyler, O., Cauchy Spaces II: Regular Completions and Compactifications, Math. Ann. 187 (1970), 187-199.
  • [32] Rath, N., Precauchy spaces, PH.D. Thesis, Washington State University, 1994.
  • [33] Rath, N., Completion of a Cauchy space without the T2-restriction on the space. Int. J. Math. Math. Sci. 3, 24 (2000), 163-172.
  • [34] Weck-Schwarz, S., T0-objects and separated objects in topological categories. Quaestiones Math. 14 (1991), 315-325.

Year 2018, Volume: 6 Issue: 2, 28 - 37, 31.10.2018

Muammer Kula , Sümeyye Kula

https://doi.org/10.36753/mathenot.476787

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., Stacks and filters. Turkish J. of Math.-Do˘ga. 16 (1992), 95-108.
  • [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., A notion of compactness in topological categories. Publ. Math. Debrecen. 50 (3-4), 221-234, 1997.
  • [7] Baran, M., T3 and T4-objects in topological categories. Indian J. Pure Appl. Math. 29 (1), 59-69, 1998.
  • [8] Baran, M., Closure operators in convergence spaces. Acta Math. Hungar. 87 (2000), 33-45.
  • [9] Baran, M., Compactness, perfectness, separation, minimality and closedness with respect to closure operators. Applied Categorical Structures. 10 (2002), 403-415.
  • [10] Baran, M., PreT2-objects in topological categories. Applied Categorical Structures. 17 (2009), 591-602, DOI 10.1007/s10485-008-9161-4.
  • [11] Baran, M. and Altındi¸s, H., T2-objects in topological categories. Acta Math. Hungar. 71 (1996), no. 1-2, 41-48.
  • [12] Baran, M. and Kula, M., A note on separation and compactness in categories of convergence spaces. Proceedings of the International Conference on Applicable General Topology (Ankara, 2001). Appl. Gen. Topol. 4 (1), 1-13, 2003.
  • [13] Bentley, H. L., Herrlich, H. and Lowen-Colebunders, E., Convergence. J. Pure Appl. Algebra. 68 (1990), no 1-2, 27-45.
  • [14] Dikranjan, D. and Giuli, E. Closure operators I. Topology Appl. 27 (1987), 129-143.
  • [15] Johnstone, P.T., Topos Theory. London Math. Soc. Monographs. No. 10, Academic Press, New York, 1977.
  • [16] Katˇetov, M., On continuity structures and spaces of mappings. Comm. Math. Univ. Car. 6 (1965), 257-278.
  • [17] Keller, H., Die Limes-uniformisierbarkeit der Limesräume. Math. Ann. 176 (1968), 334-341.
  • [18] Kent, D. C. and Richardson, G. D., Cauchy Spaces with Regular Completions. Pacific J. Math. 3 (1984), 105-116.
  • [19] Kent, D. C. and Richardson, G. D., Cauchy Completion Categories. Canad. Math. Bull. 32 (1989), 78-83.
  • [20] Kowalsky, H. J., Limesräume und Komplettierung. Math. Nachr. 12 (1954), 301-340.
  • [21] Kula, M., A Note on Cauchy Spaces. Acta Math. Hungar. 133 (2011), no. 1-2, 14-32, DOI:10.1007/s10474-011- 0136-9.
  • [22] Kula, M., Separation properties at p for the topological category of Cauchy Spaces. Acta Math. Hungar. 136 (2012), no. 1-2, 1-15, DOI: 10.1007/s10474-012-0238-z.
  • [23] Kula, M., T3 and T4-Objects in the Topological Category of Cauchy Spaces. Communications, Series A1:Mathematics and Statistics. 66 (2017), no. 1, 29-42.
  • [24] Lowen-Colebunders, E., Function classes of Cauchy Continuous maps M. Dekker, New York, 1989.
  • [25] Marny, Th., Rechts-Bikategoriestrukturen in topologischen Kategorien. Dissertation, Freie Universität Berlin, 1973.
  • [26] Mielke, M.V., Separation axioms and geometric realizations. Indian J. Pure Appl. Math. 25 (1994), 711-722.
  • [27] Munkres, J. R., Topology:A First Course, Prentice-Hall, 1975.
  • [28] Nel, L. D., Initially structured categories and cartesian closedness. Canad. Journal of Math. XXVII (1975), 1361-1377.
  • [29] Preuss, G., Theory of Topological Structures. An Approach to Topological Categories., D. Reidel Publ. Co., Dordrecht, 1988.
  • [30] Preuss, G., Improvement of Cauchy spaces. Q&A in General Topology. 9 (1991), 159-166.
  • [31] Ramaley, J. F. andWyler, O., Cauchy Spaces II: Regular Completions and Compactifications, Math. Ann. 187 (1970), 187-199.
  • [32] Rath, N., Precauchy spaces, PH.D. Thesis, Washington State University, 1994.
  • [33] Rath, N., Completion of a Cauchy space without the T2-restriction on the space. Int. J. Math. Math. Sci. 3, 24 (2000), 163-172.
  • [34] Weck-Schwarz, S., T0-objects and separated objects in topological categories. Quaestiones Math. 14 (1991), 315-325.
There are 34 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Muammer Kula 0000-0002-1366-6149

Sümeyye Kula This is me 0000-0001-5185-2877

Publication Date October 31, 2018
Submission Date May 2, 2018
Acceptance Date August 14, 2018
Published in Issue Year 2018 Volume: 6 Issue: 2

Cite

APA Kula, M., & Kula, S. (2018). Tychonoff Objects in the Topological Category of Cauchy Spaces. Mathematical Sciences and Applications E-Notes, 6(2), 28-37. https://doi.org/10.36753/mathenot.476787
AMA Kula M, Kula S. Tychonoff Objects in the Topological Category of Cauchy Spaces. Math. Sci. Appl. E-Notes. October 2018;6(2):28-37. doi:10.36753/mathenot.476787
Chicago Kula, Muammer, and Sümeyye Kula. “Tychonoff Objects in the Topological Category of Cauchy Spaces”. Mathematical Sciences and Applications E-Notes 6, no. 2 (October 2018): 28-37. https://doi.org/10.36753/mathenot.476787.
EndNote Kula M, Kula S (October 1, 2018) Tychonoff Objects in the Topological Category of Cauchy Spaces. Mathematical Sciences and Applications E-Notes 6 2 28–37.
IEEE M. Kula and S. Kula, “Tychonoff Objects in the Topological Category of Cauchy Spaces”, Math. Sci. Appl. E-Notes, vol. 6, no. 2, pp. 28–37, 2018, doi: 10.36753/mathenot.476787.
ISNAD Kula, Muammer - Kula, Sümeyye. “Tychonoff Objects in the Topological Category of Cauchy Spaces”. Mathematical Sciences and Applications E-Notes 6/2 (October 2018), 28-37. https://doi.org/10.36753/mathenot.476787.
JAMA Kula M, Kula S. Tychonoff Objects in the Topological Category of Cauchy Spaces. Math. Sci. Appl. E-Notes. 2018;6:28–37.
MLA Kula, Muammer and Sümeyye Kula. “Tychonoff Objects in the Topological Category of Cauchy Spaces”. Mathematical Sciences and Applications E-Notes, vol. 6, no. 2, 2018, pp. 28-37, doi:10.36753/mathenot.476787.
Vancouver Kula M, Kula S. Tychonoff Objects in the Topological Category of Cauchy Spaces. Math. Sci. Appl. E-Notes. 2018;6(2):28-37.

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