T3 AND T4-objects in the topological category of cauchy spaces

Muammer Kula

doi:10.1501/Commua1_0000000772

T3 AND T4-objects in the topological category of cauchy spaces

Year 2017, Volume: 66 Issue: 1, 29 - 42, 01.02.2017

Muammer Kula

https://doi.org/10.1501/Commua1_0000000772

Cited By: 1

Keywords

Topological category, Cauchy space, Cauchy map, separation

References

J. Adámek, H. Herrlich, and G. E. Strecker, Abstract and Concrete Categories, Wiley, New York, 1990.
M. Baran, Separation properties, Indian J. Pure Appl. Math., 23 (1992), 333-341.
M. Baran, Stacks and …lters, Turkish J. of Math.-Do¼ga, 16 (1992), 95-108.
M. Baran, The notion of closedness in topological categories, Comment. Math. Univ. Caroli- nae, 34 (1993), 383-395.
M. Baran, T-ob jects in categories of …lter and local …lter convergence spaces, Turkish J. of Math.-Do¼ga, 20 (1996), 159-168.
M. Baran, Completely Regular Ob jects and Normal Ob jects in topological categories, Acta Math. Hungar., 80 (1998), no. 3, 211-224.
M. Baran, T3and T4-ob jects in topological categories, Indian J. Pure Appl. Math., 29 (1998), 59-69.
M. Baran, Closure operators in convergence spaces, Acta Math. Hungar., 87 (2000), 33-45.
M. Baran, Compactness, perfectness, separation, minimality and closedness with respect to closure operators, Applied Categorical Structures, 10 (2002), 403-415.
M. Baran, PreT2-ob jects in topological categories, Applied Categorical Structures, 17 (2009), 602, DOI 10.1007/s10485-008-9161-4.
M. Baran and H. Altındi¸s, To-Ob jects in Topological Categories, J. Univ. Kuwait (sci.), 22 (1995), 123-127.
M. Baran and H. Altındi¸s, T-ob jects in topological categories, Acta Math. Hungar., 71 (1996), no. 1-2, 41-48.
M. Baran and M. Kula, A note on separation and compactness in categories of convergence spaces, Applied General Topology, 4 (2003), no. 1, 1-13.
M. Baran, D. Tokat and M. Kula, Connectedness and separation in the category of closure spaces, Filomat, 24 (2010), 67-79.
H. L. Bentley, H. Herrlich, and E. Lowen-Colebunders, Convergence, J. Pure Appl. Algebra, (1990), no 1-2, 27-45.
D. Dikranjan and E. Giuli, Closure operators I, Topology Appl., 27 (1987), 129-143.
R. Friµc and D. Kent, On the natural completion functor for Cauchy spaces, Bull. Austral. Math. Soc., 18 (1978), 335-343.
R. Friµc and D. Kent, Completion functors for Cauchy spaces, Internat. J. Math. and Math. Sci. 2, 4 (1979), 589-604.
S. Gähler, W. Gähler, and G. Kneis, Completion of pseudotopological vector spaces, Math., Nachr., 75 (1976), 185-206.
P.T. Johnstone, Topos Theory, London Math. Soc. Monographs, No. 10, Academic Press, New York, 1977.
M. Katµetov, On continuity structures and spaces of mappings, Comm. Math. Univ. Car., 6 (1965), 257-278.
H. Keller, Die Limes-uniformisierbarkeit der Limesräume, Math. Ann., 176 (1968), 334-341.
D. C. Kent and G. D. Richardson, Cauchy Spaces with Regular Completions, Paci…c J. Math., (1984), 105-116.
D. C. Kent and G. D. Richardson, Cauchy Completion Categories, Canad. Math. Bull, 32 (1989), 78-83.
G. Kneis, On regular completion of pseudo-uniform spaces, Colloquia Math. Soc. János Bolyai, 23 (1978), 713-727.
H. J., Kowalsky, Limesräume und Komplettierung, Math. Nachr., 12 (1954), 301-340.
M. Kula, A Note on Cauchy Spaces, Acta Math. Hungar., 133 (2011), no. 1-2, 14-32, DOI:10.1007/s10474-011-0136-9.
M. Kula, 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.
E. Lowen-Colebunders, On the regularity of the Kowalsky completion, Canad. J. Math., 36 (1984), 58-70.
E. Lowen-Colebunders, Function classes of Cauchy Continuous maps, M. Dekker, New York, Th. Marny, Rechts-Bikategoriestrukturen in topologischen Kategorien, Dissertation, Freie Universität Berlin, 1973.
M.V. Mielke, Separation axioms and geometric realizations, Indian J. Pure Appl. Math., 25 (1994), 711-722.
L. D. Nel, Initially structured categories and cartesian closedness, Canad. Journal of Math., XXVII (1975), 1361-1377.
G. Preuss, Theory of Topological Structures. An Approach to Topological Categories, D. Reidel Publ. Co., Dordrecht, 1988.
G. Preuss, Improvement of Cauchy spaces, Q&A in General Topology, 9 (1991), 159-166.
J. F. Ramaley and O. Wyler, Cauchy Spaces II: Regular Completions and Compacti…cations, Math. Ann., 187 (1970), 187-199.
N. Rath, Precauchy spaces, PH.D. Thesis, Washington State University, 1994.
N. Rath, Completion of a Cauchy space without the T-restriction on the space, Int. J. Math. Math. Sci., 3, 24 (2000), 163-172.
E. Reed, Completion of uniform convergence spaces, Math. Ann., 194 (1971), 83-108.
S. Weck-Schwarz, T0-ob jects and separated ob jects in topological categories, Quaestiones Math., 14 (1991), 315-325.
Current address : Department of Mathematics, Faculty of Science, Erciyes University, Kayseri Turkey. E-mail address : kulam@erciyes.edu.tr

Year 2017, Volume: 66 Issue: 1, 29 - 42, 01.02.2017

Muammer Kula

https://doi.org/10.1501/Commua1_0000000772

Cited By: 1

References

J. Adámek, H. Herrlich, and G. E. Strecker, Abstract and Concrete Categories, Wiley, New York, 1990.
M. Baran, Separation properties, Indian J. Pure Appl. Math., 23 (1992), 333-341.
M. Baran, Stacks and …lters, Turkish J. of Math.-Do¼ga, 16 (1992), 95-108.
M. Baran, The notion of closedness in topological categories, Comment. Math. Univ. Caroli- nae, 34 (1993), 383-395.
M. Baran, T-ob jects in categories of …lter and local …lter convergence spaces, Turkish J. of Math.-Do¼ga, 20 (1996), 159-168.
M. Baran, Completely Regular Ob jects and Normal Ob jects in topological categories, Acta Math. Hungar., 80 (1998), no. 3, 211-224.
M. Baran, T3and T4-ob jects in topological categories, Indian J. Pure Appl. Math., 29 (1998), 59-69.
M. Baran, Closure operators in convergence spaces, Acta Math. Hungar., 87 (2000), 33-45.
M. Baran, Compactness, perfectness, separation, minimality and closedness with respect to closure operators, Applied Categorical Structures, 10 (2002), 403-415.
M. Baran, PreT2-ob jects in topological categories, Applied Categorical Structures, 17 (2009), 602, DOI 10.1007/s10485-008-9161-4.
M. Baran and H. Altındi¸s, To-Ob jects in Topological Categories, J. Univ. Kuwait (sci.), 22 (1995), 123-127.
M. Baran and H. Altındi¸s, T-ob jects in topological categories, Acta Math. Hungar., 71 (1996), no. 1-2, 41-48.
M. Baran and M. Kula, A note on separation and compactness in categories of convergence spaces, Applied General Topology, 4 (2003), no. 1, 1-13.
M. Baran, D. Tokat and M. Kula, Connectedness and separation in the category of closure spaces, Filomat, 24 (2010), 67-79.
H. L. Bentley, H. Herrlich, and E. Lowen-Colebunders, Convergence, J. Pure Appl. Algebra, (1990), no 1-2, 27-45.
D. Dikranjan and E. Giuli, Closure operators I, Topology Appl., 27 (1987), 129-143.
R. Friµc and D. Kent, On the natural completion functor for Cauchy spaces, Bull. Austral. Math. Soc., 18 (1978), 335-343.
R. Friµc and D. Kent, Completion functors for Cauchy spaces, Internat. J. Math. and Math. Sci. 2, 4 (1979), 589-604.
S. Gähler, W. Gähler, and G. Kneis, Completion of pseudotopological vector spaces, Math., Nachr., 75 (1976), 185-206.
P.T. Johnstone, Topos Theory, London Math. Soc. Monographs, No. 10, Academic Press, New York, 1977.
M. Katµetov, On continuity structures and spaces of mappings, Comm. Math. Univ. Car., 6 (1965), 257-278.
H. Keller, Die Limes-uniformisierbarkeit der Limesräume, Math. Ann., 176 (1968), 334-341.
D. C. Kent and G. D. Richardson, Cauchy Spaces with Regular Completions, Paci…c J. Math., (1984), 105-116.
D. C. Kent and G. D. Richardson, Cauchy Completion Categories, Canad. Math. Bull, 32 (1989), 78-83.
G. Kneis, On regular completion of pseudo-uniform spaces, Colloquia Math. Soc. János Bolyai, 23 (1978), 713-727.
H. J., Kowalsky, Limesräume und Komplettierung, Math. Nachr., 12 (1954), 301-340.
M. Kula, A Note on Cauchy Spaces, Acta Math. Hungar., 133 (2011), no. 1-2, 14-32, DOI:10.1007/s10474-011-0136-9.
M. Kula, 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.
E. Lowen-Colebunders, On the regularity of the Kowalsky completion, Canad. J. Math., 36 (1984), 58-70.
E. Lowen-Colebunders, Function classes of Cauchy Continuous maps, M. Dekker, New York, Th. Marny, Rechts-Bikategoriestrukturen in topologischen Kategorien, Dissertation, Freie Universität Berlin, 1973.
M.V. Mielke, Separation axioms and geometric realizations, Indian J. Pure Appl. Math., 25 (1994), 711-722.
L. D. Nel, Initially structured categories and cartesian closedness, Canad. Journal of Math., XXVII (1975), 1361-1377.
G. Preuss, Theory of Topological Structures. An Approach to Topological Categories, D. Reidel Publ. Co., Dordrecht, 1988.
G. Preuss, Improvement of Cauchy spaces, Q&A in General Topology, 9 (1991), 159-166.
J. F. Ramaley and O. Wyler, Cauchy Spaces II: Regular Completions and Compacti…cations, Math. Ann., 187 (1970), 187-199.
N. Rath, Precauchy spaces, PH.D. Thesis, Washington State University, 1994.
N. Rath, Completion of a Cauchy space without the T-restriction on the space, Int. J. Math. Math. Sci., 3, 24 (2000), 163-172.
E. Reed, Completion of uniform convergence spaces, Math. Ann., 194 (1971), 83-108.
S. Weck-Schwarz, T0-ob jects and separated ob jects in topological categories, Quaestiones Math., 14 (1991), 315-325.
Current address : Department of Mathematics, Faculty of Science, Erciyes University, Kayseri Turkey. E-mail address : kulam@erciyes.edu.tr

There are 40 citations in total.

Details

Primary Language	English
Journal Section	Research Articles
Authors	Muammer Kula This is me
Publication Date	February 1, 2017
Published in Issue	Year 2017 Volume: 66 Issue: 1

Cite

APA	Kula, M. (2017). T3 AND T4-objects in the topological category of cauchy spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 66(1), 29-42. https://doi.org/10.1501/Commua1_0000000772
AMA	Kula M. T3 AND T4-objects in the topological category of cauchy spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2017;66(1):29-42. doi:10.1501/Commua1_0000000772
Chicago	Kula, Muammer. “T3 AND T4-Objects in the Topological Category of Cauchy Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66, no. 1 (February 2017): 29-42. https://doi.org/10.1501/Commua1_0000000772.
EndNote	Kula M (February 1, 2017) T3 AND T4-objects in the topological category of cauchy spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66 1 29–42.
IEEE	M. Kula, “T3 AND T4-objects in the topological category of cauchy spaces”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 66, no. 1, pp. 29–42, 2017, doi: 10.1501/Commua1_0000000772.
ISNAD	Kula, Muammer. “T3 AND T4-Objects in the Topological Category of Cauchy Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66/1 (February 2017), 29-42. https://doi.org/10.1501/Commua1_0000000772.
JAMA	Kula M. T3 AND T4-objects in the topological category of cauchy spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66:29–42.
MLA	Kula, Muammer. “T3 AND T4-Objects in the Topological Category of Cauchy Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 66, no. 1, 2017, pp. 29-42, doi:10.1501/Commua1_0000000772.
Vancouver	Kula M. T3 AND T4-objects in the topological category of cauchy spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66(1):29-42.

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