On some unifications
by
T. Hatice Yalvac

Some authors have been studying on unification theories in topological spaces as in [1, 11, 12, 13, 14, 15, 16, 17, 19, 20, 22, 23, 24]. It was studied to unify continuities, opennes, closedness, compactness, filters and graphs in [22, 23, 24]. It will be given some known and unknown results obtained from these papers. For example it was given in [18] 33 equivalent statement to almost strongly \Theta-semi-continuity defined in [5] and 44 equivalent statement to weak \delta-continuity defined in [4].

Referenes

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[2] M.E.Abd El-Monsef, E.F.Lashien, Local discrete extensions of supratopologies. Tamkang J. Math. 21, No.1(1990), 1-6.

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[4] C. W. Baker, On super continuous functions, Bull. Korean Math. Soc., 22 (1985), 17-22.

[5] Y. Beceren, S. Yüksel, E. Hatýr, On almost strongly \Theta-semi-continuous functions, Bull. Cal. Math. Soc. 87, (1987), 329-334

[6] J. Dugundji, Topology, (1966).

[7] I.L. Herrington and P.E. Long, Characerizations of H-closed spaces, Proc. Amer. Math. Soc. 48(1987), 367-376.

[8] S. Jafari, T. Noiri, On strongly \Theta-semi-continuous functions, Indian J. pure appl. Math., 29, 11 (1998), 1195-1201.

[9] S. Jafari, T. Noiri, On almost strongly \Theta-semi-continuous functions, Acta Math. Hungar. 85, 1-2 (1999), 167-173.

[10]. Jafari, T. Noiri, Some properties of almost S-continuous functions, Rend. Circ. Mat. Palermo, II. XLVIII (1999), 571-582.

[11] D. S. Jankovi\'c, On functions with \alpha-closed graphs, Glasnik Matematck, 18, No. 38(1983), 141-148.

[12] A. Kandil, E. E. Kerre and A. A. Nouh, Operations and mappings on fuzzy topological spaces, Ann. Soc. Sci. Bruxelles 105, No. 4. (1991), 165-168.

[13] S. Kasahara, Operation-compact spaces, Math. Japonica 24, No. 1 (1979), 97-105.

[14] E. E. Kerre, A. A. Nouh and A. Kandil, Operations on the class of fuzzy sets on a universe endowed with a fuzzy topology, J. Math. Anal. Appl. 180 (1993), 325-341.

[15] J. K. Kohli, A class of mappings containing all continuous and all semiconnected mappings, Proc. Amer. Math. Soc. 72, No. 1 (1978), 175-181.

[16] J. K. Kohli, A framework including the theories of continuities and certain non-continuous functions, Note di Mat. 10, No. 1 (1990), 37-45.

[17] J. K. Kohli, Change of topology, characterizations and product theorems for semi-localy P-spaces, Houston J. Math. 17, No. 3 (1991), 335-349.

[18] I. Kökdemir, Unification of week continuities and strong continuities, M. Sc Thesiss, Hacettepe Unv., January 2000.

[19] M. N. Mukherjee and G. Sengupta, On \pi-closedness: A unified theory, Anal. Sti. Univ. Ä\i. I. Cuza" Iasi, 39, s. 1.a, Mat. No. 3 (1993), 1-10.

[20] G. Sengupta and M. N. Mukherjee, On \pi-closedness a unified theory II, Boll. U. M. I. 7, 8-B (1994), 999-1013.

[21] T. H. Yalvac, Relations between new topologies obtained from old ones, Acta Math. Hungar. 64, No. 3 (1994) , 231-235.

[22] T. H. Yalvac A unified theory for continuities, submitted.

[23] T. H. Yalvac A unified theory on openness and closedness of functions, submitted.

[24] T. H. Yalvac A unified theory on compactness and filters, submitted.

Date received: June 30, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caeh-50.