Related papers: The tie theorems

In this article, we demonstrate the common fixed point theorems for three transformations on vector S-metric space by utilizing weakly compatible and point of coincidence. Moreover, some of our results generalize the existing results in the…

We take points and planes as fundamental, lines as derived, in an axiomatic formulation of three-dimensional projective space, the self-dual nature of which formulation renders automatic the principle of duality.

We show that if an orientation-preserving homeomorphism of the plane has a topologically chain recurrent point, then it has a fixed point, generalizing the Brouwer plane translation theorem.

Using a new point of view inspired by hyperplane arrangements, we generalize the converse to Pascal's Theorem, sometimes called the Braikenridge-Maclaurin Theorem. In particular, we show that if 2k lines meet a given line, colored green, in…

If P is a point inside triangle ABC, then the cevians through P extended to the circumcircle of triangle ABC create a figure containing a number of curvilinear triangles. Each curvilinear triangle is bounded by an arc of the circumcircle…

Given a family of based CW-pairs $(\underline{X},\underline{A})=\{(X;A)\}^m_{i=1}$ together with an abstract simplicial complex $K$ with $m$ vertices, there is an associated based CW-complex $Z(K;(\underline{X},\underline{A}))$ known as a…

Erd\H{o}s-Beck theorem states that $n$ points in the plane with at most $n-x$ points collinear define at least $c xn$ lines for some positive constant $c$. In this paper, we will present two ways to extend this result to higher dimensions.…

In this paper a generalized topological central point theorem is proved for maps of a simplex to finite-dimensional metric spaces. Similar generalizations of the Tverberg theorem are considered.

The primary objects of study in the ``knot theory of complex plane curves'' are C-links: links (or knots) cut out of a 3-sphere in the complex plane by complex plane transverse and totally tangential. Transverse C-links are naturally…

In this paper, we introduce the notion of partially ordered {\epsilon}-chainable metric spaces and we derive new coupled fixed point theorems for uniformly locally contractive mappings on such spaces.

Tensor diagrams are a handy way to depict complicated relationships between objects in projective geometry. One of the simpler ones takes two copies of a $3\times 3$ matrix and computes its adjugate. In this paper, we give a geometric…

This article provides a new perspective on the geometry of a projective line, which helps clarify and illuminate some classical results about projective plane. As part of the same train of ideas, the article also provides a proof of the…

We introduce the notion of cylinder of a relation in the context of posets, extending the construction of the mapping cylinder. We establish a local-to-global result for relations, generalizing Quillen's Theorem A for order preserving maps,…

This work is a continuation of [1]. As in the previous article, here we will describe some interesting ideas and a lot of new theorems in plane geometry related to them.

Tree-like tableaux are combinatorial objects that appear in a combinatorial understanding of the PASEP model from statistical mechanics. In this understanding, the corners of the Southeast border correspond to the locations where a particle…

Kelly's theorem states that a set of $n$ points affinely spanning $\mathbb{C}^3$ must determine at least one ordinary complex line (a line passing through exactly two of the points). Our main theorem shows that such sets determine at least…

In this paper, we give some requirements under which two self-mappings have a common fixed point in $b$-metric-like spaces.

This article examines the coincidence of the projective and conformal Weyl tensors associated to a given connection D. The connection may be a general Weyl connection associated to a conformal class of metrics [g]. The main result for n>3…

A projective rectangle is like a projective plane that has different lengths in two directions. We develop the basic theory of projective rectangles including incidence properties, projective subplanes, configuration counts, a partial…

We present a unitary approach to the construction of representations and intertwining operators. We apply it to the $C^*$-algebras, groups, Gabor type unitary systems and wavelets. We give an application of our method to the theory of…