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Proceedings of the American Mathematical Society

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

 

 

Equivalence of certain discontinuous functions under closure


Author: Maurice Hugh Miller
Journal: Proc. Amer. Math. Soc. 54 (1976), 384-388
Erratum: Proc. Amer. Math. Soc. 61 (1976), 187.
MathSciNet review: 0390142
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Abstract: We show that no distinction can be made between the closure of a Darboux graph and the closure of a connected graph, and under certain conditions, we show the closure of a Darboux function is the closure of an almost continuous function. In showing this, a construction process is given to show how to turn certain non-almost continuous functions into almost continuous functions.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0390142-8
Keywords: Darboux function, connected function, almost continuous function
Article copyright: © Copyright 1976 American Mathematical Society