PreprintarXiv licencearXiv
Tight σ-filtrations and the BFPP of C(ω*)
Abstract
Assuming that 𝒫(ω) is tightly σ-filtered, we prove that C(ω*) fails the ball fixed point property. This axiom holds under the continuum hypothesis and in the ℵ2-Cohen model. The proof shows that the Stone space of the countable--cocountable algebra Cc(ω1) is a continuous retract of ω* and uses the equivalence between tight σ-filteredness of Cc(ω1) and of 𝒫(ω). We also prove that the quotient of a tightly σ-filtered Boolean algebra B with the countable separation property by an ℵ1-generated P-ideal is a Boolean retract of B.
Related
- F-nilpotence and Hodge filtrations beyond isolated singularities
- Holomorphic polyvector fields on toric varieties via Klyachko filtrations
- Filtrations on Local Cohomology and Injectivity Theorems
- Multivariate V-filtrations and the Strong Monodromy Conjecture for hyperplane arrangements
- Calculating Hodge and weight filtrations on localizations
BibTeX
@misc{aviles2026tight,
title = {{Tight $σ$-filtrations and the BFPP of $C(ω^*)$}},
author = {Antonio Avilés and Maurício Rossetto},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16672},
eprint = {2610.16672},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16672},
}
RIS
TY - UNPB
TI - Tight σ-filtrations and the BFPP of C(ω^*)
AU - Antonio Avilés
AU - Maurício Rossetto
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16672
UR - https://arxiv.org/abs/2610.16672
AB - Assuming that 𝒫(ω) is tightly σ-filtered, we prove that C(ω^*) fails the ball fixed point property. This axiom holds under the continuum hypothesis and in the ℵ_2-Cohen model. The proof shows that the Stone space of the countable--cocountable algebra Cc(ω_1) is a continuous retract of ω^* and uses the equivalence between tight σ-filteredness of Cc(ω_1) and of 𝒫(ω). We also prove that the quotient of a tightly σ-filtered Boolean algebra B with the countable separation property by an ℵ_1-generated P-ideal is a Boolean retract of B.
ER -