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Refinements of the density and $ \mathcal{I}$-density topologies


Authors: Krzysztof Ciesielski and Lee Larson
Journal: Proc. Amer. Math. Soc. 118 (1993), 547-553
MSC: Primary 26A99; Secondary 54H99
DOI: https://doi.org/10.1090/S0002-9939-1993-1129874-2
MathSciNet review: 1129874
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Abstract: Given an arbitrary ideal $ \mathcal{J}$ on the real numbers, two topologies are defined that are both finer than the ordinary topology. There are nonmeasurable, non-Baire sets that are open in all of these topologies, independent of $ \mathcal{J}$. This shows why the restriction to Baire sets is necessary in the usual definition of the $ \mathcal{J}$-density topology. It appears to be difficult to find such restrictions in the case of an arbitrary ideal.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1129874-2
Keywords: Density topology, $ \mathcal{J}$-density topology, fine topologies
Article copyright: © Copyright 1993 American Mathematical Society

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