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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A class of mappings containing all continuous and all semiconnected mappings

Author: J. K. Kohli
Journal: Proc. Amer. Math. Soc. 72 (1978), 175-181
MSC: Primary 54C05
MathSciNet review: 0493941
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Abstract: A function $ f:X \to Y$ is called s-continuous if for each $ x \in X$ and each open set V containing $ f(x)$ and having connected complement there is an open set U containing x such that $ f(U) \subset V$. In this paper basic properties of s-continuous functions are studied; conditions on domain and/or range implying continuity of s-continuous functions are obtained which generalize recent theorems of Jones, Lee and Long on semiconnected functions. Improvements of recent results of Hagan, Kohli and Long concerning the continuity of certain connected functions follow as a consequence. Also characterizations of semilocally connected spaces in terms of s-continuous functions are obtained.

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Keywords: s-continuous function, (weak) semiconnected function, open function, closed function, connected function, monotone function, graph function, closed graph, saturated space, semilocally connected space
Article copyright: © Copyright 1978 American Mathematical Society