Related papers: Correction to the paper "Some remarks on Davie's u…
This paper has been withdrawn by the author due to an error in the use of the Cauchy-Kowalevski theorem in section 4., theorem 4.1 which does not allow to prove the final result. When (and if) this error will be cured it will be replaced by…
This paper has been withdrawn by the author for further investigation.
In this work, new equivalences of topological statements and weaker axioms than ${\bf AC}$ are proven. This equivalences include the use of anti-properties. All this equivalences have been checked with a computer using the theorem proving…
We correct the statements of two theorems and two corollaries in our paper [On subgroup perfect codes in Cayley graphs, European J. Combin. 91 (2021) 103228]. Proofs of these theorems and three other results are given as well.
This note presents a unified theorem of the alternative that explicitly allows for any combination of equality, componentwise inequality, weak dominance, strict dominance, and nonnegativity relations. The theorem nests 60 special cases,…
In the revised version of the paper, we correct misprints and add some new statements.
We point out an essential gap in the proof of one of main results in \cite{M} and then give a corrected proof for it.
We show that every inclusion of von Neumann algebras with a faithful normal conditional expectation has the weak relative Dixmier property. This answers a question of Popa \cite{Po99}. The proof uses an improvement of Ellis' lemma for…
First a few reformulations of Frankl's conjecture are given, in terms of reduced families or matrices, or analogously in terms of lattices. These lead naturally to a stronger conjecture with a neat formulation which might be easier to…
This paper has been withdrawn by the authors due to a mistake in the proof of Theorem 1.
In this paper, we strengthen the splitting theorem proved in [14, 15] and provide a different approach using ideas from the weak KAM theory.
In Phys. Rev. Lett. 113, 120404 (2014) [arXiv:1403.2362], Ferrie and Combes claim that weak values could be a statistical artifact caused by correlations between the disturbance and the post-selection condition imposed on the output. In…
We discuss published assertions concerning fixed points in digital metric spaces that are incorrect or incorrectly proven, or reduce to triviality.
The paper is withdrawn by the authors and replaced be an improved and extended version arxiv: 0812.2968
We give a pen and paper and (comparatively) much simpler proof to verify of the Four Colour Theorem.
We show that there is a restriction, or modification of the finite-variable fragments of First Order Logic in which a weak form of Craig's Interpolation Theorem holds, but a strong form of this theorem does not hold. Translating these…
There is an irreparable error in the proof of Theorem 3.26 in our "Model Theory of Fields with Virtually Free Group Actions" paper and we withdraw the claim of having proved that theorem. In fact, that theorem is false in a very strong…
In this note, we point out an error in the proof of Theorem 4.7 of [P. Achar and A.~Henderson, `Orbit closures in the enhanced nilpotent cone', Adv. Math. 219 (2008), 27-62], a statement about the existence of affine pavings for fibres of a…
This note corrects a minor misstatement in section 2 of the paper in the title (arXiv:0808.3426). It also addresses some related issues. The error does not affect the main results of that paper, but nevertheless this corrigendum seems…
We here reply to a recent comment by Vaidman [\href{https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.5.048001}{Phys. Rev. Res. 5, 048001 (2023)}] on our paper…