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• W2023135644 abstract "In 1922 Blumberg[1] introduced the notion of a real valued function on Euclidean space being densely approached at a point in its domain. Continuous functions satisfy this condition at each point of their domains. This concept was generalized by Ptak[7] in 1958 who used the term ’nearly continuous’, and by Husain[3] in 1966 under the name of ’almost continuity’. More recently, Mashhour et al. [5] have called this property of functions between arbitrary topological spaces ’precontinuity’. In this paper we define a new property of functions between topological spaces which is the dual of Blumberg’s original notion, in the sense that together they are equivalent to continuity. Thus we provide a new decomposition of continuity in Theorem 4 (iv) which is of some historical interest. In a recent paper [10] , Tong introduced the notion of an A–set in a topological space and the concept of A–continuity of functions between topological spaces. This enabled him to produce a new decomposition of continuity. In this paper we improve Tong’s decomposition result and provide a decomposition of A–continuity." @default.
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• W2023135644 date "1990-09-01" @default.
• W2023135644 modified "2023-09-26" @default.
• W2023135644 title "A decomposition of continuity" @default.
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• W2023135644 doi "https://doi.org/10.1007/bf01903846" @default.
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