TY  - JOUR
T1  - Tychonoff Objects in the Topological Category of Cauchy Spaces
AU  - Kula, Muammer
AU  - Kula, Sümeyye
PY  - 2018
DA  - October
Y2  - 2018
DO  - 10.36753/mathenot.476787
JF  - Mathematical Sciences and Applications E-Notes
JO  - Math. Sci. Appl. E-Notes
PB  - Murat TOSUN
WT  - DergiPark
SN  - 2147-6268
SP  - 28
EP  - 37
VL  - 6
IS  - 2
LA  - en
KW  - Topological category
KW  - Cauchy space
KW  - Cauchy map
KW  - Separation
CR  - [1] Adámek, J., Herrlich, H. and Strecker, G. E., Abstract and Concrete Categories, Wiley, New York, 1990.
CR  - [2] Baran, M., Separation properties. Indian J. Pure Appl. Math. 23 (1992), 333-341.
CR  - [3] Baran, M., Stacks and filters. Turkish J. of Math.-Do˘ga. 16 (1992), 95-108.
CR  - [4] Baran, M., The notion of closedness in topological categories. Comment. Math. Univ. Carolinae. 34 (1993), 383-395.
CR  - [5] Baran, M., Generalized Local Separation Properties. Indian J. Pure Appl. Math. 25 (1994), 615-620.
CR  - [6] Baran, M., A notion of compactness in topological categories. Publ. Math. Debrecen. 50 (3-4), 221-234, 1997.
CR  - [7] Baran, M., T3 and T4-objects in topological categories. Indian J. Pure Appl. Math. 29 (1), 59-69, 1998.
CR  - [8] Baran, M., Closure operators in convergence spaces. Acta Math. Hungar. 87 (2000), 33-45.
CR  - [9] Baran, M., Compactness, perfectness, separation, minimality and closedness with respect to closure operators.
Applied Categorical Structures. 10 (2002), 403-415.
CR  - [10] Baran, M., PreT2-objects in topological categories. Applied Categorical Structures. 17 (2009), 591-602, DOI
10.1007/s10485-008-9161-4.
CR  - [11] Baran, M. and Altındi¸s, H., T2-objects in topological categories. Acta Math. Hungar. 71 (1996), no. 1-2, 41-48.
CR  - [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.
CR  - [13] Bentley, H. L., Herrlich, H. and Lowen-Colebunders, E., Convergence. J. Pure Appl. Algebra. 68 (1990), no 1-2,
27-45.
CR  - [14] Dikranjan, D. and Giuli, E. Closure operators I. Topology Appl. 27 (1987), 129-143.
CR  - [15] Johnstone, P.T., Topos Theory. London Math. Soc. Monographs. No. 10, Academic Press, New York, 1977.
CR  - [16] Katˇetov, M., On continuity structures and spaces of mappings. Comm. Math. Univ. Car. 6 (1965), 257-278.
CR  - [17] Keller, H., Die Limes-uniformisierbarkeit der Limesräume. Math. Ann. 176 (1968), 334-341.
CR  - [18] Kent, D. C. and Richardson, G. D., Cauchy Spaces with Regular Completions. Pacific J. Math. 3 (1984), 105-116.
CR  - [19] Kent, D. C. and Richardson, G. D., Cauchy Completion Categories. Canad. Math. Bull. 32 (1989), 78-83.
CR  - [20] Kowalsky, H. J., Limesräume und Komplettierung. Math. Nachr. 12 (1954), 301-340.
CR  - [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.
CR  - [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.
CR  - [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.
CR  - [24] Lowen-Colebunders, E., Function classes of Cauchy Continuous maps M. Dekker, New York, 1989.
CR  - [25] Marny, Th., Rechts-Bikategoriestrukturen in topologischen Kategorien. Dissertation, Freie Universität Berlin,
1973.
CR  - [26] Mielke, M.V., Separation axioms and geometric realizations. Indian J. Pure Appl. Math. 25 (1994), 711-722.
CR  - [27] Munkres, J. R., Topology:A First Course, Prentice-Hall, 1975.
CR  - [28] Nel, L. D., Initially structured categories and cartesian closedness. Canad. Journal of Math. XXVII (1975),
1361-1377.
CR  - [29] Preuss, G., Theory of Topological Structures. An Approach to Topological Categories., D. Reidel Publ. Co.,
Dordrecht, 1988.
CR  - [30] Preuss, G., Improvement of Cauchy spaces. Q&A in General Topology. 9 (1991), 159-166.
CR  - [31] Ramaley, J. F. andWyler, O., Cauchy Spaces II: Regular Completions and Compactifications, Math. Ann. 187
(1970), 187-199.
CR  - [32] Rath, N., Precauchy spaces, PH.D. Thesis, Washington State University, 1994.
CR  - [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.
CR  - [34] Weck-Schwarz, S., T0-objects and separated objects in topological categories. Quaestiones Math. 14 (1991),
315-325.
UR  - https://doi.org/10.36753/mathenot.476787
L1  - https://dergipark.org.tr/en/download/article-file/564527
ER  -