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Proceedings of the American Mathematical Society

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

 
 

 

Almost continuous real functions


Authors: K. R. Kellum and B. D. Garrett
Journal: Proc. Amer. Math. Soc. 33 (1972), 181-184
MSC: Primary 26A21; Secondary 54C50
DOI: https://doi.org/10.1090/S0002-9939-1972-0293026-5
MathSciNet review: 0293026
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Abstract: A blocking set of a function f is a closed set which does not intersect f but which intersects each continuous function with domain the same as f. It is shown that for each function which is not almost continuous, there exists a minimal blocking set. Using this property it is shown that there exists an almost continuous function with domain [0, 1] which is a $ {G_\delta }$ set but is not of Baire Class 1, and that there exists an almost continuous function dense in the unit square.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0293026-5
Keywords: Connected function, connectivity function, almost continuous
Article copyright: © Copyright 1972 American Mathematical Society

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