TL;DR
This paper provides a straightforward solution to a question about the structure of I-positive Borel sets within ccc sigma-ideals, specifically regarding the existence of I-positive closed subsets.
Contribution
It offers a simple answer to a previously open problem about the relationship between I-positive Borel sets and I-positive closed sets in ccc sigma-ideals.
Findings
Confirmed that for ccc sigma-ideals, I-positive Borel sets contain I-positive closed sets modulo the ideal.
Provided a concise solution to Question 7.2.7 from prior literature.
Abstract
The aim of this short note is to communicate a simple solution to the problem posed in [1] as Question 7.2.7: is it true that for every ccc -ideal I any I-positive Borel set contains modulo I an I-positive closed set?
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Taxonomy
TopicsAdvanced Topology and Set Theory · Advanced Banach Space Theory · Fuzzy and Soft Set Theory