Related papers: A local Jordan-Brouwer separation theorem
We give a new proof of the Krohn-Rhodes Theorem using local divisors. The proof provides nearly as good a decomposition in terms of size as the holonomy decomposition of Eilenberg, avoids induction on the size of the state set, and works…
All known Moufang sets arise, in some way or another, from an algebraic structure which can be called `division' in some way. In this PhD dissertation, I made an attempt to develop a theory of local Moufang sets, which generalize Moufang…
We study local splitting-type results for general Loday algebroids and use them to obtain a direct proof of the splitting theorem for Courant algebroids. We also discuss the linearization problem and establish a general linearization…
We prove a local version of the Mazur-Ulam theorem.
Here is present short proofing of Jordan's theorem about dividing of flat on two disjoint subsets by one closed curve.
A new proof of the decomposition theorem is established using a relation with a version of the local purity theorem of Deligne and Gabber adapted to complex algebraic varieties.
A conjecture for higher order separation on generic rational surfaces with some new results about standard divisors.
We present a new proof of the classical divergence theorem in bounded domains. Our proof is based on a nonlocal analog of the divergence theorem and a rescaling argument. Main ingredients in the proof are nonlocal versions of the divergence…
Among diversity of frameworks and constructions introduced in Loewner Theory by different authors, one can distinguish two closely related but still different ways of reasoning, which colloquially may be described as "increasing" and…
We present some results and conjectures on a generalization to the noncommutative setup of the Brouwer fixed-point theorem from the Borsuk-Ulam theorem perspective.
We prove relative versions of many earlier results about almost invariant sets and splittings of groups. In particular, we prove a relative version of the algebraic torus theorem, and we prove the existence and uniqueness of relative…
We develop the local Morse theory for a class of non-twice continuously differentiable functionals on Hilbert spaces, including a new generalization of the Gromoll-Meyer's splitting theorem and a weaker Marino-Prodi perturbation type…
We develop the local Morse theory for a class of non-twice continuously differentiable functionals on Hilbert spaces, including a new generalization of the Gromoll-Meyer's splitting theorem and a weaker Marino-Prodi perturbation type…
We prove a generalization of the Jordan canonical form theorem for a class of bounded linear operators on complex separable Hilbert spaces.
In this paper we study the existence and continuation of solution to general fractional differential equation with Hilfer fractional derivative. First we establish new local existence theorems. Then we derive the continuation theorems. With…
We prove the Jordan curve theorem by generalizing the sweepline algorithm for trapezoidal decomposition of a polygon. Our proof uses Zorn's lemma (or, equivalently the axiom of choice). Though several proofs have been given for the Jordan…
We present a solution of Exercise 1.2.1 of [2] which yields a short new proof of a key step in one of proofs of Brouwer's fixed point theorem, 1910. A few people asked the author about the details of the solution and they might be…
We discuss various forms of the classical van der Corput's difference theorem and explore applications to and connections with the theory of uniform distribution, ergodic theory, topological dynamics and combinatorics.
Based on the reduction of degree in polynomial mappings and some known results in algebraic geometry, by introducing the Brouwer degree, a tool from differential topology, algebraic topology and algebraic geometry, we completely prove the…
We present a concise proof for the supporting hyperplane theorem. We then observe that the proof not only establishes the supporting hyperplane theorem but also extends it to a hyperplane separation theorem for certain non-convex sets. The…