Real Analysis Exchange

Maximally Resolvable Lower Density Spaces

David Rose and Ben Thurston

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We show that all measure based and all category based lower density topologies on $\mathbb{R}$ are maximally resolvable in $\mathbf{ZFC}$ and extraresolvable under $\mathbf{ZFC + MA}$. It is also noted that both maximal resolvability and extraresolvability are feeble topological properties

Article information

Real Anal. Exchange Volume 33, Number 2 (2007), 475-482.

First available in Project Euclid: 18 December 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 28A05: Classes of sets (Borel fields, $\sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05] 54A10: Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)
Secondary: 54C08: Weak and generalized continuity

measure based lower density space category based lower density space maximal resolvability extraresolvability feeble topological property feeble homeomorphism


Rose, David; Thurston, Ben. Maximally Resolvable Lower Density Spaces. Real Anal. Exchange 33 (2007), no. 2, 475--482.

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