Tootfinder

Tietze extension does not always work in constructive mathematics if closed sets are defined as sequentially closed sets
Shun Ding, Yang Wan, Luofei Wang, Siqi Xiao
https://arxiv.org/abs/2508.11635

Tietze extension does not always work in constructive mathematics if closed sets are defined as sequentially closed sets
We prove that Tietze Extension does not always exist in constructive mathematics if closed sets on which the function we are extending are defined as sequentially closed sets. Firstly, we take a discrete metric space as our topological space. Now all sets open and sequentially closed. Then, we form an unextendible algorithmic function transforming positive integers to 0 and 1, looking at the preimages of these values as our sequentially closed sets. Then we show that if the Tietze theorem concl…

What is happening here? F-35s for fighting against drugs traffickers is very strange. An attack against Venezuela would be a good distraction for Trump from everything that is going wrong elsewhere.
https://www.twz.com/air/10-f-35s-deploying

Dynamical neutron-star tides: The signature of a mode resonance
P. Pnigouras, N. Andersson, F. Gittins, A. R. Counsell
https://arxiv.org/abs/2508.06416 https://

Dynamical neutron-star tides: The signature of a mode resonance
Motivated by future opportunities in gravitational-wave astronomy and the ongoing effort to constrain physics under extreme conditions, we consider the signature of individual mode resonances excited during the inspiral of binary systems involving neutron stars. Specifically, we quantify how each resonant mode contributes to the effective (frequency-dependent) tidal deformability. The resonant solution is shown to be accurately represented by a new closed-form approximation, which sheds light o…

Quasi-Periodic Eruptions as a Probe of Accretion Disk in Tidal Disruption Events
Tomoya Suzuguchi, Tatsuya Matsumoto
https://arxiv.org/abs/2509.01663 https://

Quasi-Periodic Eruptions as a Probe of Accretion Disk in Tidal Disruption Events
Quasi-periodic eruptions (QPEs) are X-ray transients characterized by nearly regular recurring flares from galactic nuclei. Recent observations have confirmed that some QPEs occur in galactic centers that experienced a tidal disruption event (TDE) a few years earlier. This may be reasonably explained if QPEs are produced when a star orbiting a supermassive black hole passes through an accretion disk formed by the TDE. Based on this scenario, we investigate the expected QPE signatures in the ear…