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PreprintarXiv licencearXiv

There Are Exactly 2c Simultaneously Bireflective and Bicoreflective Subconstructs of FTS

  • Gao Zhang
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Abstract

We prove that there are exactly 2c simultaneously bireflective and bicoreflective subconstructs of 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 2c ultrafilters on ℕ into total fuzzy topologies contained in M.

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Cite

BibTeXRIS
BibTeX
@misc{zhang2026there,
  title = {{There Are Exactly $2^\mathfrakc$ Simultaneously Bireflective and Bicoreflective Subconstructs of $\mathbfFTS$}},
  author = {Gao Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.35876},
  eprint = {2610.35876},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.35876},
}
RIS
TY  - UNPB
TI  - There Are Exactly 2^c Simultaneously Bireflective and Bicoreflective Subconstructs of FTS
AU  - Gao Zhang
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.35876
UR  - https://arxiv.org/abs/2610.35876
AB  - We prove that there are exactly 2^c simultaneously bireflective and bicoreflective subconstructs of 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^c ultrafilters on ℕ into total fuzzy topologies contained in M.
ER  -