math. sci. appl. e-notes Mathematical Sciences and Applications E-Notes 2147-6268 Murat TOSUN 10.36753/mathenot.476787 Tychonoff Objects in the Topological Category of Cauchy Spaces https://orcid.org/0000-0002-1366-6149 Kula Muammer https://orcid.org/0000-0001-5185-2877 Kula Sümeyye 10 31 2018 6 2 28 37 05 02 2018 08 14 2018 Copyright © 2013, Mathematical Sciences and Applications E-Notes 2013 Mathematical Sciences and Applications E-Notes Topological category Cauchy space Cauchy map Separation 1 [1] Adámek, J., Herrlich, H. and Strecker, G. E., Abstract and Concrete Categories, Wiley, New York, 1990. 2 [2] Baran, M., Separation properties. Indian J. Pure Appl. Math. 23 (1992), 333-341. 3 [3] Baran, M., Stacks and filters. Turkish J. of Math.-Do˘ga. 16 (1992), 95-108. 4 [4] Baran, M., The notion of closedness in topological categories. Comment. Math. Univ. Carolinae. 34 (1993), 383-395. 5 [5] Baran, M., Generalized Local Separation Properties. Indian J. Pure Appl. Math. 25 (1994), 615-620. 6 [6] Baran, M., A notion of compactness in topological categories. Publ. Math. Debrecen. 50 (3-4), 221-234, 1997. 7 [7] Baran, M., T3 and T4-objects in topological categories. Indian J. Pure Appl. Math. 29 (1), 59-69, 1998. 8 [8] Baran, M., Closure operators in convergence spaces. Acta Math. Hungar. 87 (2000), 33-45. 9 [9] Baran, M., Compactness, perfectness, separation, minimality and closedness with respect to closure operators. Applied Categorical Structures. 10 (2002), 403-415. 10 [10] Baran, M., PreT2-objects in topological categories. Applied Categorical Structures. 17 (2009), 591-602, DOI 10.1007/s10485-008-9161-4. 11 [11] Baran, M. and Altındi¸s, H., T2-objects in topological categories. Acta Math. Hungar. 71 (1996), no. 1-2, 41-48. 12 [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 [13] Bentley, H. L., Herrlich, H. and Lowen-Colebunders, E., Convergence. J. Pure Appl. Algebra. 68 (1990), no 1-2, 27-45. 14 [14] Dikranjan, D. and Giuli, E. Closure operators I. Topology Appl. 27 (1987), 129-143. 15 [15] Johnstone, P.T., Topos Theory. London Math. Soc. Monographs. No. 10, Academic Press, New York, 1977. 16 [16] Katˇetov, M., On continuity structures and spaces of mappings. Comm. Math. Univ. Car. 6 (1965), 257-278. 17 [17] Keller, H., Die Limes-uniformisierbarkeit der Limesräume. Math. Ann. 176 (1968), 334-341. 18 [18] Kent, D. C. and Richardson, G. D., Cauchy Spaces with Regular Completions. Pacific J. Math. 3 (1984), 105-116. 19 [19] Kent, D. C. and Richardson, G. D., Cauchy Completion Categories. Canad. Math. Bull. 32 (1989), 78-83. 20 [20] Kowalsky, H. J., Limesräume und Komplettierung. Math. Nachr. 12 (1954), 301-340. 21 [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 [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 [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 [24] Lowen-Colebunders, E., Function classes of Cauchy Continuous maps M. Dekker, New York, 1989. 25 [25] Marny, Th., Rechts-Bikategoriestrukturen in topologischen Kategorien. Dissertation, Freie Universität Berlin, 1973. 26 [26] Mielke, M.V., Separation axioms and geometric realizations. Indian J. Pure Appl. Math. 25 (1994), 711-722. 27 [27] Munkres, J. R., Topology:A First Course, Prentice-Hall, 1975. 28 [28] Nel, L. D., Initially structured categories and cartesian closedness. Canad. Journal of Math. XXVII (1975), 1361-1377. 29 [29] Preuss, G., Theory of Topological Structures. An Approach to Topological Categories., D. Reidel Publ. Co., Dordrecht, 1988. 30 [30] Preuss, G., Improvement of Cauchy spaces. Q&A in General Topology. 9 (1991), 159-166. 31 [31] Ramaley, J. F. andWyler, O., Cauchy Spaces II: Regular Completions and Compactifications, Math. Ann. 187 (1970), 187-199. 32 [32] Rath, N., Precauchy spaces, PH.D. Thesis, Washington State University, 1994. 33 [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 [34] Weck-Schwarz, S., T0-objects and separated objects in topological categories. Quaestiones Math. 14 (1991), 315-325.