REVIEW
Sets completely separated by functions in Bishop Set Theory
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
read the original abstract
Within Bishop Set Theory, a reconstruction of Bishop's theory of sets, we study the so-called completely separated sets, that is sets equipped with a positive notion of an inequality, induced by a given set of real-valued functions. We introduce the notion of a global family of completely separated sets over an index-completely separated set, and we describe its Sigma- and Pi-set. The free completely separated set on a given set is also presented. Purely set-theoretic versions of the classical Stone-\v{C}ech theorem and the Tychonoff embedding theorem for completely regular spaces are given, replacing topological spaces with function spaces and completely regular spaces with completely separated sets.
Discussion (0). Continue with ORCID to comment.