1. Inserting measurable functions precisely
- Creator:
- Gutiérrez García, Javier and Kubiak, Tomasz
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- insertion, $\sigma $-topology, $\sigma $-ring, perfectness, normality, upper measurable function, lower measurable function, and measurable function
- Language:
- English
- Description:
- 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public