Refinements of the density and -density topologies

Authors:
Krzysztof Ciesielski and Lee Larson

Journal:
Proc. Amer. Math. Soc. **118** (1993), 547-553

MSC:
Primary 26A99; Secondary 54H99

MathSciNet review:
1129874

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Abstract: Given an arbitrary ideal 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 . This shows why the restriction to Baire sets is necessary in the usual definition of the -density topology. It appears to be difficult to find such restrictions in the case of an arbitrary ideal.

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DOI:
https://doi.org/10.1090/S0002-9939-1993-1129874-2

Keywords:
Density topology,
-density topology,
fine topologies

Article copyright:
© Copyright 1993
American Mathematical Society