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 is called *s*-continuous if for each and each open set *V* containing and having connected complement there is an open set *U* containing *x* such that . 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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1978-0493941-9

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