Closedness of certain classes of functions in the topology of uniform convergence

• Autorzy: Kohli J. K. , Aggarwal J.
• Języki publikacji: EN

Abstrakty

EN

In this paper, closedness of certain classes of functions in VX in the topology of uniform convergence is observed. In particular, we show that the function spaces SC(X, Y) of quasi continuous (…) functions, (…) (X, Y ) of (…)-continuous functions and L(X,Y) of cl-supercontinuous functions are closed in YX in the topology of uniform convergence.

Słowa kluczowe

EN

semi-open set; cl-open set; uniform space; topology of uniform convergence

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2012
• Tom: Vol. 45, nr 4
• Strony: 947--952
• Opis fizyczny: Bibliogr. 21 poz.

Twórcy

autor

Kohli J. K.

autor

Aggarwal J.

• Department Of Mathematics Hindu College University Of Delhi Delhi 110007, India,

Bibliografia

• [1] S.P.Arya, M.Deb, On mappings almost continuous in the sense of Frolík Math. Student 41 (1973), 311-321.
• [2] E.Ekici, Generalization of perfectly continuous, regular set-connected and clopen functions Acta Math.Hungar. 107(3) (2005), 193-206.
• [3] E.Ekici, V.Popa, Some properties of upper and lower clopen continuous multifunctions Bul. Stint. Univ. Politeh. Timis. Ser. Mat. Fiz. 50(64) (2005), 1-11.
• [4] Z.Frolik, Remarks concerning the invariance of Baire spaces under mappings Czechoslovak Math.J. 11(3) (1961), 381-385.
• [5] K.R.Gentry, H.B.Hoyle, III,Somewhat continuous functions Czechoslovak Math. J.21(1) (1971), 5-12.
• [6] H.B.Hoyle, III, Function spaces for somewhat continuous functions Czechoslovak Math.J. 21(1) (1971), 31-34.
• [7] J.L.Kelley, General Topology D.Van Nostrand Company, New York, 1955.
• [8] S.Kempisty, Sur les fonctions quasicontnues Fund.Math.19 (1932), 184-197.
• [9] J.K.Kohli, A class of spaces containing all connected and all locally connected spaces Math. Nachr. 82(1978), 121-129.
• [10] J.K.Kohli, D.Singh, Function spaces and strong variants of continuity Appl.Gen. Topol. 9(1) (2008), 33-38.
• [11] J.K.Kohli, D.Singh, Almost cl-supercontinuous functions Appl.Gen.Topol.10(1) (2009), 1-12.
• [12] N.Levine, Semi-open sets and semi-continuity in topological spaces Amer.Math. Monthly 70 (1963), 36-41.
• [13] A.S.Mashhour, I.A.Hasanein, S.N.El Deeb, _-continuous and _-open mappings Acta Math.Hungar.41 (1983), 213-218.
• [14] S.A.Naimpally, Function space topologies for connectivity and semiconnectivity functions Canad. Math. Bull.9 (1966), 349-352.
• [15] S.A.Naimpally, Graph topology for function spaces Trans. Amer. Math.Soc.123 (1966), 267-272.
• [16] S.A.Naimpally, On strongly continuous functions Amer. Math. Monthly 74 (1967), 166-169.
• [17] O.Njastad, On some classes of nearly open sets Pacic J.Math.15 (1965), 961-970.
• [18] I.L.Reilly, M.K.Vamanamurthy, On supercontinuous mappings Indian J.Pure Appl. Math. 14(6) (1983), 767-772.
• [19] W.Sierpiński, Sur une propriété de fonctions réelles quelconques Matematiche (Catania) 8 (1953), 43-48.
• [20] D.Singh, cl-supercontinuous functions Appl.Gen.Topol.8(2)(2007), 293-300.
• [21] J.R.Stallings, Fixed point theorems for connectivity maps Fund. Math.47 (1959), 249-263.