Related papers: Orthogonally connected sets
In this paper, we deal with analytic and geometric properties of orthogonally convex sets. We establish a Blaschke-type theorem for path-connected and orthogonally convex sets in the plane using orthogonally convex paths. The separation of…
A graph is said to be orthogonalisable if the set of real symmetric matrices whose off-diagonal pattern is prescribed by its edges contains an orthogonal matrix. We determine some necessary and some sufficient conditions on the sizes of the…
Using the orthogonal connectedness, we introduce the notion of orthogonal decomposability of convex polytopes and study it in the case of Platonic and Archimedean solids. While doing so, we also encounter polytopes which are not…
This note describes necessary and sufficient conditions for a sequence of positive integers to be the degree sequence of a connected simple graph. Conditions are also given under which a sequence is necessarily connected i.e. the sequence…
An orthogonality space is a set equipped with a symmetric, irreflexive relation called orthogonality. Every orthogonality space has an associated complete ortholattice, called the logic of the orthogonality space. To every poset, we…
Necessary and sufficient conditions for a sequence of positive integers to be the degree sequence of a k-connected simple graph are detailed. Conditions are also given under which such a sequence is necessarily k-connected.
In this paper we give necessary and sufficient conditions for a connection in a plane bundle above a surface to be locally metric. These conditions are easy to be verified in any local chart. Also as a global result we give a necessary…
This paper continues the investigation of staircases in the family of Hirzebruch surfaces formed by blowing up the projective plane with weight b, that was started in Bertozzi, Holm et al. in arXiv:2010.08567. We explain the symmetries…
The soft topological spaces and some their related concepts have stud- ied in [7]. In this paper, we introduce and study the notions of soft connected topological spaces after a review of preliminary definitions.
Necessary and sufficient conditions for a sequence of positive integers to be the degree sequence of a 3-connected simple graph are detailed. Conditions are also given under which such a sequence is necessarily 3-connected i.e. the sequence…
This paper proves a Kolmogorov-complexity-flavored sufficient condition for a set to be attractive and discusses some consequences of this condition.
Though a convergence space is connected if and only if its topological modification is connected, connected subsets differ for the convergence and for its topological modification. We explore for what subsets connectedness for the…
In the literature, various types of points and meager sets whose complements are connected have been studied, such as colocally connected points, non-weak cut points/sets, non-block points/sets, shore points/sets, etc. We extend that study,…
This note gives necessary and sufficient conditions for a sequence of non-negative integers to be the degree sequence of a connected simple graph. This result is implicit in a paper of Hakimi. A new alternative characterisation of these…
We study the sets of planes in an even dimensional real vector space $V$ which are simultaneously stabilised by a pair of complex structures on $V$. We completely describe these sets of planes for pairs of orthogonal complex structures.…
We establish necessary and sufficient conditions for a dynamical system to be topologically conjugate to the Morse minimal set, the shift orbit closure of the Morse sequence, and conditions for topological conjugacy to the closely related…
Skeleton is a new notion designed for constructing space-filling curves of self-similar sets. It is shown in [Dai, Rao and Zhang, Space-filling curves of self-similar sets (II): Edge-to-trail substitution…
We examine the question whether random set attractors for continuous-time random dynamical systems on a connected state space are connected. In the deterministic case, these attractors are known to be connected. In the probabilistic setup,…
We introduce a geometric construction which relates to the pentagram map much in the way that a logarithmic spiral relates to a circle. After introducing the construction, we establish some basic geometric facts about it, and speculate on…
In this article one builds a class of recursive sets, one establishes properties of these sets, and one proposes applications.