Related papers: On some extension theorems for multifunctions
The aim of this short note is to give counterexamples to two results by D. Y. Gao [5, Th. 16], [4, Th. 2] and to improve a related result by S.-C. Fang, D. Y. Gao, R.-L. Sheu and S.-Y. Wu [1, Th. 3].
In this short note we present a family of counterexamples to the King's conjecture.
We first exhibit counterexamples to some open questions related to a theorem of Sakai. Then we establish an extension theorem of Sakai type for separately holomorphic/meromorphic functions.
We give a counterexample to a recently conjectured variant of the Penrose inequality.
We prove several extensions of the Erdos-Fuchs theorem.
This paper has been withdrawn by the author(s) and included into the new version of "An extension theorem for separately holomorphic functions with singularities", math.CV/0104089.
We present new counterexamples, which provide stronger limitations to sums-differences statements than were previously known. The main idea is to consider non-uniform probability measures.
In this paper, we intend to revisit Theorem 2 of [3] formulating it in a way that, weakening the hypotheses and, at the same time, highlighting the richer conclusion allowed by the proof, it can potentially be applicable to a broader range…
In this note I provide two extensions of a particular case of the classical Poncelet theorem.
In this note we provide important and significant observations in ring theory related to weakly tripotent rings. We provide counterexamples for the structure theorem for commutative weakly tripotent rings appeared in arXiv (2017) and Bull.…
We show how our recent results on compositions of d.c. functions (and mappings) imply positive results on extensions of d.c. functions (and mappings). Examples answering two natural relevant questions are presented. Two further theorems,…
The paper presents a counterexample to the Hodge conjecture.
In this very short note, we give a counterexample to a recent conjecture of Gilmer which would have implied the union-closed conjecture.
In this paper we give simple extension and uniqueness theorems for restricted additive and logarithmic functional equations.
We prove extension-dimensional versions of finite dimensional selection and approximation theorems. As applications, we obtain several results on extension dimension.
We prove some extensions of Andrews inequality.
This survey article gives an account of quasiconformal extensions of univalent functions with its motivational background from Teichm\"uller theory and classical and modern approaches based on Loewner theory.
We discuss the (twisted) weak positivity theorem. We also treat some applications.
We give alternative proofs to certain results in the paper "Weak limits of almost invariant projections" by using ultraproducts of operators.
In this paper, we give a counter-example, in the general case, Kronecker theorem will derive contradiction. Kronecker theorem be correct after removing some conditions.