Year: 2026
Type: article
Abstract: We prove that it is consistent with ZFC that for every non-decreasing function f : [ 0 , 1 ] → [ 0 , 1 ] $f:[0,1]\rightarrow [0,1]$ f colon left bracket 0 comma 1 right bracket right arrow left bracket 0 comma 1 right bracket , each subset of [ 0 , 1 ] $[0,1]$ left bracket 0 comma 1 right bracket of cardinality c $\mathfrak c$ German c contains a set of cardinality c $\mathfrak c$ German c on which f is uniformly continuous. We show that this statement follows from the assumptions that d ∗ < c $\mathfrak d^* <\mathfrak c$ German d Superscript asterisk Baseline less than German c and c $\mathfrak c$ German c is regular, where d ∗ ≤ d $\mathfrak d^*\leq \mathfrak d$ German d Superscript asterisk Baseline less than or equals German d is the smallest cardinality
Source: Journal of Symbolic Logic
Authors: ROMAN POL, PIOTR ZAKRZEWSKI, LYUBOMYR ZDOMSKYY
Institutions: University of Warsaw, TU Wien
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
Funder: Austrian Science Fund
Award: G9001302138
OpenAlex ID: W6947914833
FWCI:
Cites:
Cited by:
Related to: