Related papers: On some extensions of Morley's trisector theorem

In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…

In this paper, we first prove that the absorption law for one-sided inverses along an element holds, deriving the absorption law for the inverse along an element. We then apply this result to obtain the absorption law for the inverse along…

We consider the method of alternating projections for finding a point in the intersection of two closed sets, possibly nonconvex. Assuming only the standard transversality condition (or a weaker version thereof), we prove local linear…

Motivated by the study of a certain family of classical geometric problems we investigate the existence of multiplicative connections on proper Lie groupoids. We show that one can always deform a given connection which is only approximately…

Most of the assertions in the theory of well ordered sets are quite simple. However, one of its central statements, Zermelo's theorem, stands out of this rule, for its well-known proofs are rather complicated. The aim of the current paper…

A brief introduction to the theory of ordered sets and lattice theory is given. To illustrate proof techniques in the theory of ordered sets, a generalization of a conjecture of Daykin and Daykin, concerning the structure of posets that can…

We prove a generalization of the Monge-Cayley-Salmon theorem on osculation and ruled submanifolds using elementary geometric measure theory.

In this note I provide two extensions of a particular case of the classical Poncelet theorem.

The authors give a complete classification of projective threefolds admitting a holomorphic normal projective connection. Moreover, they prove a general structure theorem on complex projective manifolds admitting a holomorphic normal…

In this short note we give counterexamples to several results related to extension theorems published recently.

It is proved that a triangulation of a polyhedron can always be transformed into any other triangulation of the polyhedron by using only elementary moves. One consequence is that an additive function (valuation) defined only on simplices…

We consider a generalization of the classic Sperner lemma. This lemma states that every Sperner coloring of a triangulation of a simplex contains a fully colored simplex. We found a weaker assumption than Sperner's coloring. It is also…

In this paper we consider a construction in an arbitrary triangulated category T which resembles the notion of a Moore spectrum in algebraic topology. Namely, given a compact object C of T satisfying some finite tilting assumptions, we…

We prove an extension of the Cheeger-M\"{u}ller theorem to spaces with isolated conical singularities: the $L^2$-analytic torsion coincides with the Ray-Singer intersection torsion on an even dimensional space, and they are trivial, while…

In extension theory, in particular in dimension theory, it is frequently useful to represent a given compact metrizable space X as the limit of an inverse sequence of compact polyhedra. We are going to show that, for the purposes of…

We prove some general theorems for preserving Dependent Choice when taking symmetric extensions, some of which are unwritten folklore results. We apply these to various constructions to obtain various simple consistency proofs.

A very simple and short proof of the polynomial matrix spectral factorization theorem (on the unit circle as well as on the real line) is presented, which relies on elementary complex analysis and linear algebra.

Many proofs of the Fundamental Theorem of Algebra, including various proofs based on the theory of analytic functions of a complex variable, are known. To the best of our knowledge, this proof is different from the existing ones.

It is shown in our earlier paper that, using only tools of elementary geometry, the classical Routh's theorem for triangles can be fully extended to tetrahedra. In this article we first give another proof of Routh's theorem for tetrahedra…

Transseries in the sense of \'Ecalle are constructed using a topological approach. A general contractive mapping principle is formulated and proved, showing the closure of transseries under a wide class of operations. In the second part we…