There Are Exactly $2^\mathfrak{c}$ Simultaneously Bireflective and Bicoreflective Subconstructs of $\mathbf{FTS}$

arXiv:2610.35876v1 Announce Type: new 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 $M$.

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