Related papers: On a generalization of compact and connected space…

We introduce the class of outerspatial 2-complexes as the natural generalisation of the class of outerplanar graphs to three dimensions. Answering a question of O-joung Kwon, we prove that a locally 2-connected 2-complex is outerspatial if…

It is shown that for any Baire space $X$, linearly ordered compact spaces $Y_1,\dots, Y_n$, compact space $Y\subseteq Y_1\times\cdots \times Y_n$ such that for every parallelepiped $W\subseteq Y_1\times\cdots \times Y_n$ the set $Y\cap W$…

In this note we introduce generalised pairs from the perspective of the evolution of the notion of space in birational algebraic geometry. We describe some applications of generalised pairs in recent years and then mention a few open…

The notions of compactness and Hausdorff separation for generalized enriched categories allow us, as classically done for the category $\mathsf{Top}$ of topological spaces and continuous functions, to study $\textit{compactly generated…

We examine generalized global symmetries as a kind of compactly supported cohomology, and so are led to revisit questions about the locality of quantum field theory, following Segal. Physics naturally suggests a generalization of…

We define a natural compactification of an arrangement complement in a ball quotient. We show that when this complement has a moduli space interpretation, then this compactification is often one that appears naturally by means of geometric…

This brief review is intended to introduce gravitational physicists to recent developments in which general relativity is being used to describe certain aspects of condensed matter systems, e.g., superconductivity.

We study the generalized analogues of conics for normed planes by using the following natural approach: It is well known that there are different metrical definitions of conics in the Euclidean plane. We investigate how these definitions…

As a generalization of singular linear spaces, we introduce the concept of t-singular linear spaces, make some anzahl formulas of subspaces, and determine the suborbits of t-singular linear groups.

By using the representational power of Chu spaces we define the notion of a generalized topological space (or GTS, for short), i.e., a mathematical structure that generalizes the notion of a topological space. We demonstrate that these…

We review higher-dimensional unified theories from the general relativity, rather than the particle physics side. Three distinct approaches to the subject are identified and contrasted: compactified, projective and noncompactified. We…

In this article, we consider a generalization of the conjugate Hardy $H^2$ spaces, and give some properties of the minimal norm of the generalization and some relations between the norm of the generalization and the minimal $L^2$ integrals.…

In generalization of knot quandles we introduce similar algebraic structures associated with arbitrary pairs consisting of a path-connected topological space and its path-connected subspace.

In these notes we show that any projective subspace arrangement can be realized as a generalized star configuration variety. This type of interpolation result may be useful in designing linear codes with prescribed codewords of minimum…

We present some results about spontaneous breaking of global symmetries for four-flavor, three color QCD on compact spaces with two short directions. When the two short directions have equal length and identical boundary conditions, there…

Here we will discuss the philosophical differences between an approach to the deep nature of physical space based on the concept of coordinates and one based on the concept of relation. The philosophical superiority of the second approach…

The correspondence between 2-parameter families of oriented lines in ${\Bbb{R}}^3$ and surfaces in $T{\Bbb{P}}^1$ is studied, and the geometric properties of the lines are related to the complex geometry of the surface. Congruences…

Using a technique of adjoining an order unit to a normed linear space, we have characterized strictly convex spaces among normed linear spaces and Hilbert spaces among strictly convex Banach spaces respectively. This leads to a…

The class $\mathfrak C $ relative to countably compact topological spaces and the class $\mathfrak P$ relative to pseudocompact spaces introduced by Z. Frol\'ik are naturally generalized relative to every topological property. We provide a…

In this paper, we propose a generalization of a congruence due to Carlitz.