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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.05949 |
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Table of Contents:
- Let c denote the cardinality of the continuum. Let L denote the family of all Hausdorff topologies on the real line coarser than the natural topology. We construct 2^c pairwise non-homeomorphic completely normal topologies in L among which 2^c are Baire and 2^c are of first category. We also construct c pairwise non-homeomorphic completely metrizable topologies in L. Furthermore, we investigate complete lattices of topologies in L and construct extremely long chains of homeomorphic topologies in L.