Refinements of the density and density topologies
Authors:
Krzysztof Ciesielski and Lee Larson
Journal:
Proc. Amer. Math. Soc. 118 (1993), 547553
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, nonBaire 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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 Casper Goffman and Daniel Waterman, Approximately continuous transformations, Proc. Amer. Math. Soc. 12 (1961), 116121. MR 0120327 (22:11082)
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 John C. Morgan II, Point set theory, MarcelDekker, New York, 1990. MR 1026014 (91a:54051)
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 W. Poreda, E. WagnerBojakowska, and W. Wilczyński, A category analogue of the density topology, Fund. Math. 75 (1985), 167173. MR 813753 (87b:54034)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199311298742
PII:
S 00029939(1993)11298742
Keywords:
Density topology,
density topology,
fine topologies
Article copyright:
© Copyright 1993
American Mathematical Society
