Sequential topologies and Dedekind finite sets
Jindrich Zapletal
TL;DR
This paper explores the properties of sequential topologies and Dedekind finite sets within ZF set theory, showing consistency results related to the Euclidean topology and infinite subsets of reals.
Contribution
It demonstrates the consistency of a non-sequential Euclidean topology on reals with the property that every infinite set contains a countably infinite subset, answering Gutierres' question.
Findings
Euclidean topology on reals can be non-sequential in ZF
Every infinite subset of reals can contain a countably infinite subset in this model
Addresses a specific open question in set topology
Abstract
It is consistent with ZF set theory that the Euclidean topology on the real line is not sequential, yet every infinite set of reals contains a countably infinite subset. This answers a question of Gutierres.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.