Geodesic
Inserting measurable functions precisely
Czechoslovak Mathematical Journal, Tome 64 (2014) no. 3, pp. 743-749 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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A family of subsets of a set is called a $\sigma $-topology if it is closed under arbitrary countable unions and arbitrary finite intersections. A $\sigma $-topology is perfect if any its member (open set) is a countable union of complements of open sets. In this paper perfect $\sigma $-topologies are characterized in terms of inserting lower and upper measurable functions. This improves upon and extends a similar result concerning perfect topologies. Combining this characterization with a $\sigma $-topological version of Katětov-Tong insertion theorem yields a Michael insertion theorem for normal and perfect $\sigma $-topological spaces.
A family of subsets of a set is called a $\sigma $-topology if it is closed under arbitrary countable unions and arbitrary finite intersections. A $\sigma $-topology is perfect if any its member (open set) is a countable union of complements of open sets. In this paper perfect $\sigma $-topologies are characterized in terms of inserting lower and upper measurable functions. This improves upon and extends a similar result concerning perfect topologies. Combining this characterization with a $\sigma $-topological version of Katětov-Tong insertion theorem yields a Michael insertion theorem for normal and perfect $\sigma $-topological spaces.
DOI : 10.1007/s10587-014-0128-3
Classification : 28A05, 28A20
Keywords: insertion; $\sigma $-topology; $\sigma $-ring; perfectness; normality; upper measurable function; lower measurable function; measurable function 
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Gutiérrez García, Javier; Kubiak, Tomasz. Inserting measurable functions precisely. Czechoslovak Mathematical Journal, Tome 64 (2014) no. 3, pp. 743-749. doi: 10.1007/s10587-014-0128-3

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