Related papers: Contractbility of Outer space: reprise

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 note, necessary and sufficient conditions are obtained for unilateral weighted shifts to be near subnormal . As an application of the main results, many answers to the Hilbert space problem 160 are presented at the end of the paper.

Quantum information experiments applying quantum optics in outer space with a very long baseline may have advantages over the current earth-bound experiments or the earth-to-satellite experiments because they can minimize the loss in light…

We provide a short proof of the 1-dimensional flat chain conjecture.

In this note we shall give a new proof to a quadrature formulae due to Newton.

We give a reformulation of the inverse shadowing property with respect to the class of all pseudo-orbits. This reformulation bears witness to the fact that the property is far stronger than might initially seem. We give some implications of…

An technically interesting proof of a known theorem.

Popular wisdom amongst theoretical physicists says that the continuum structure of spacetime is probably not elementary, but rather emergent. While many arguments to support that view arise from speculative ideas, the argument can also be…

This is the extended version of a talk presented at the J.W.Goethe Universitaet Frankfurt a. M. and at the same time a preview at a forthcoming extensive publication on the same subject. It is shown that there is a common background…

We prove that the road space of an R-special tree is contractible and that a locally metrizable space containing a copy of an uncountable $\omega_1$-compact subspace of a tree is not. We also raise some questions about possible…

We show that gravitational energy expression simplifies when a new set of coordinates that satisfies a certain asymptotic gauge condition is used. Compared to the ADM formula, positivity of the energy is more transparent in this new…

A short, fairly self-contained proof is given of the Poincar\'e Conjecture. In the previous version there was an error on Page 8. This gap has now been filled.

A modified version of this paper is under process and with a new title and abstract. Hence, this version of the article is completely withdrawn.

We provide a general contractibility criterion for subsets of Riemannian metrics on the disc. For instance, this result applies to the space of metrics that have positive Gauss curvature and make the boundary circle convex (or geodesic).…

In this note we give a detailed proof of a theorem of Aubin.

We present a short and self-contained proof of the extension property for partial isometries of the class of all finite metric spaces.

We present a short and self-contained proof of the choosability version of Brooks' theorem.

We prove that the complement of a closed set S satisfying an extended exterior sphere condition is nothing but the union of closed balls with common radius. This generalizes [11, Theorem 3] where the set S is assumed to be prox-regular, a…

In a present note we give a new proof of Etingof-Kazhdan quantization theorem.

The paper describes a cover of the future cover of a sofic shift which is canonical in the same way as the future cover itself. In some cases the cover is isomorphic to the future cover and in other it is a genuine extension.