On $(g,s)$-Continuous and $(\pi g,s)$-Continuous Functions
DOI:
https://doi.org/10.5644/SJM.03.1.10Abstract
New generalizations of contra-continuity called ($\pi g,s$)-continuity and ($g, s$)-continuity are presented. Characterizations and properties of ($\pi g,s$)-continuous functions are discussed.
2000 Mathematics Subject Classification. 54C05, 54C08
Downloads
References
M. E. Abd El-Monsef, S. N. El-Deeb and R. A. Mahmoud, β-open sets and β-continuous mappings, Bull. Fac. Sci. Assiut Univ., 12 (1983), 77–90.
D. Andrijevic, Semipreopen sets, Mat. Vesnik, 38 (1986), 24–32.
S. P. Arya and M. P. Bhamini, Some generalizations of pairwise Urysohn spaces, Indian J. Pure Appl. Math., 18 (1987), 1088–1093.
N. Bourbaki, General Topology, Part I, Addison Wesley, Reading, Mass 1996.
M. Caldas, S. Jafari, T. Noiri and M. Simoes, A new generalization of contracontinuity via Levine’s g-closed sets, Chaos, Solitons and Fractals, to appear.
S. H. Cho, A note on almost s-continuous functions, Kyungpook Math. J., 42 (2002), 171–175.
H. Corson and E. Michael, Metrizability of certain countable unions, Illinois J. Math., 8 (1964), 351–360.
S. G. Crossley and S. K. Hildebrand, Semi-closure, Texas J. Sci., 22 (1971), 99–112.
J. Dontchev, Contra-continuous functions and strongly S-closed spaces, Int. J. Math. Math. Sci., 19 (2) (1996), 303–310.
J. Dontchev and T. Noiri, Contra-semicontinuous functions, Math. Pannonica, 10 (1999), 159–168.
J. Dontchev, M. Ganster and I. Reilly, More on almost s-continuity, Indian J. Math., 41 (1999), 139–146.
J. Dontchev and T. Noiri, Quasi-normal and πg-closed sets, Acta Math. Hungar., 89 (3) (2000), 211–219.
E. Ekici, On contra R-continuity and a weak form, Indian J. Math., 46 (2–3) (2004), 267–281.
E. Ekici, Almost contra-super-continuous functions, Studii si Cercetari Stiintifice, Seria: Matematica, Univ. din Bacau, 14 (2004), 31–42.
E. Ekici, Properties of regular set-connected functions, Kyungpook Math. J., 44 (2004), 395–403.
E. Ekici, Another form of contra-continuity, Kochi J. Math., 1 (2006), 21–29.
E. Ekici and C. W. Baker, On πg-closed sets and continuity, Kochi J. Math., accepted. [18] E. Ekici, On contra πg-continuous functions, to appear.
M. Ganster, On strongly s-regular spaces, Glasnik Mat., 25 (45) (1990), 195–201.
S. Jafari and T. Noiri, Contra-super-continuous functions, Ann. Univ. Sci. Budapest E¨otv¨os Sect. Math., 42 (1999), 27-34.
J. E. Joseph and M. H. Kwack, On S-closed spaces, Proc. Amer. Math. Soc., 80 (1980), 341–348.
N. Levine, Strong continuity in topological spaces, Amer. Math. Monthly, 67 (1960), 269.
N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70 (1963), 36–41.
N. Levine, Generalized closed sets in topology, Rend. Circ. Mat. Palermo, 19 (1970), 89–96.
G. D. Maio, S-closed spaces, S-sets and S-continuous functions, Accad. Sci. Torino, 118 (1984), 125–134.
G.Di Maio and T. Noiri, On s-closed spaces, Indian J. Pure Appl. Math., 18 (1987), 226–233.
A. S. Mashhour, M. E. Abd El-Monsef and S. N. El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt, 53 (1982), 47–53.
O. Njastad, On some classes of nearly open sets, Pacific J. Math., 15 (1965), 961–970.
T. Noiri, On S-closed subspaces, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fiz. Mat. Natur., 8 (64) (1978), 157–162.
T. Noiri, Super-continuity and some strong forms of continuity, Indian J. Pure Appl. Math., 15 (1984), 241–250.
T. Noiri, A note on S-closed spaces, Bull. Inst. Math. Acad. Sinica, 12 (1984), 229–235.
T. Noiri, On almost continuous functions, Indian J. Pure Appl. Math., 20 (1989), 571–576.
T. Noiri, B. Ahmad and M. Khan, Almost s-continuous functions, Kyungpook Math. J., 35 (1995), 311–322.
T. Noiri and S. Jafari, Properties of (θ, s)-continuous functions, Topology Appl., 123 (2002), 167–179.
M. C. Pal and P. Bhattacharyya, Faint precontinuous functions, Soochow J. Math., 21 (1995), 273–289.
T. Soundararajan, Weakly Hausdorff Spaces and the Cardinality of Topological Spaces, in: General Topology and its Relation to Modern Analysis and Algebra. III, Proc. Conf. Kanpur, 1968, Academia, Prague 1971, pp. 301–306.
L. A. Steen and J. A. Seebach Jr, Counterexamples in Topology, Holt, Rinerhart and Winston, New York 1970.
M. H. Stone, Applications of the theory of Boolean rings to general topology, TAMS, 41 (1937), 375–381.
T. Thompson, S-closed spaces, Proc. Amer. Math. Soc., 60 (1976), 335–338.
N. V. Veliˇcko, H-closed topological spaces, Amer. Math. Soc. Transl., 78 (1968), 103–118.
G. J. Wang, On S-closed spaces, Acta Math. Sinica, 24 (1981), 55–63.
V. Zaitsev, On certain classes of topological spaces and their bicompactifications, Dokl. Akad. Nauk SSSR, 178 (1968), 778–779.