There Are Exactly $2^\mathfrak{c}$ Simultaneously Bireflective and Bicoreflective Subconstructs of $\mathbf{FTS}$
Year: 2026
Type: preprint
Abstract: We prove that there are exactly $2^\mathfrak{c}$ simultaneously bireflective and bicoreflective subconstructs of $\mathbf{FTS}$. By the Lowen--Wuyts bijection, these correspond to the total fuzzy topologies contained in $M$, the fuzzy topology consisting of all nondecreasing left-continuous self-maps of the unit interval. The upper bound follows from a cardinality estimate. The matching lower bound is obtained by encoding $2^{\mathfrak c}$ ultrafilters on $\mathbb N$ into total fuzzy topologies contained in $M$.
Source: arXiv (Cornell University)
Author: Zhang, Gao
Institution: Jiangsu Second Normal University
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7224095677