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Proceedings of the American Mathematical Society

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

 

 

Sets of points of discontinuity


Author: Richard Bolstein
Journal: Proc. Amer. Math. Soc. 38 (1973), 193-197
MSC: Primary 54C30; Secondary 26A15
DOI: https://doi.org/10.1090/S0002-9939-1973-0312457-9
MathSciNet review: 0312457
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Abstract: In order that a subset $ F$ of a topological space coincide with the set of points of discontinuity of a real-valued function on the space, it is necessary that $ F$ be an $ {F_\sigma }$-set devoid of isolated points. It is shown that this condition is also sufficient if the space is ``almost-resolvable", and in particular if the space is either separable, first countable, locally compact Hausdorff, or topological linear.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0312457-9
Keywords: $ D{F_\sigma }$-space, resolvable, almost-resolvable, SI-space
Article copyright: © Copyright 1973 American Mathematical Society