Continuous maps in terms of new convergence conditions
Abstract
It is well known that if X is Frechet, then a map f : X -->Y is continuous if and only if xn --> x in X implies f(xn)--> f(x) in Y . In this paper, some new convergence conditions in terms of sequences have been introduced and in terms of these convergence conditions, generalisations and analogues of some known results of continuous maps are obtained.
Keywords: Convergence, continuous, Frechet , Sequence.
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References
[1] A. Wilansky, Topology for analysis Xerox College Publishing Lexington,Massachusetts, Toronto,1970.
[2] R. V. Fuller, Relations among continuous and various non continuous functions, Pacific J. Math. 1968. 25: 495-509.
[3] N. Liden, K-Spaces,their anti spaces and related mappings, Pacific J.Math. 1975. 50: 505-514.
[4] G. L. Garg, A. Goel, Convergence and perfect maps in metric spaces,Indian Journal of Pure and Applied Mathematics, 1996. 27(7):633-637.
[5] G. L.Garg, A. Goel, Some conditions implying continuity of Maps, Acta Math. Hungarica, 1998. 81(3): 271-274.
View more references (1)
[6] G. L.Garg, A. Goel, Continuity of Maps in terms of cluster points,International Journal Of Pure and Applied Mathematics,2009. 51:431-435.