相关论文: The Caratheodory Topology for Multiply Connected D…
The theory of complex trees is introduced as a new approach to study a broad class of self-similar sets. Systems of equations encoded by complex trees tip-to-tip equivalence relations are used to obtain one-parameter families of connected…
We prove the Pleijel theorem in non-collapsed RCD spaces, providing an asymptotic upper bound on the number of nodal domains of Laplacian eigenfunctions. As a consequence, we obtain that the Courant nodal domain theorem holds except at most…
The contour of a family of filters along a filter is a set-theoretic lower limit. Topologicity and regularity of convergences can be characterized with the aid of the contour operation. Contour inversion is studied, in particular, for…
We introduce an effective edge network theory to characterize the boundary topology of coupled edge states generated from various types of topological insulators. Two examples studied are a two-dimensional second-order topological insulator…
A behavior of homeomorphisms of Orlicz classes in a closure of a domain is investigated. It is proved that above classes are equicontinuous in the closure of domains with some restrictions on it's boundaries provided that the corresponding…
Recently, topological interfaces between three-dimensional abelian Chern-Simons theories were constructed. In this note we investigate such topological interfaces in the context of the $AdS_3/CFT_2$ correspondence. We show that it is…
We stress that in contradiction with what happens in space dimensions $n \geq 3$, there is no strict bound on the number of bound states with the same structure as the semi-classical estimate for large coupling constant and give, in two…
In this paper, we study some properties of the closure operator in the Mac\'ias topology on infinite integral domains. Moreover, under certain conditions, we present topological proofs of the infiniteness of maximal ideals and…
We prove that the pluri-fine topology on any open set $\Omega$ in $\mathbb{C}^{n}$ is locally connected. This answers a question by Fuglede in [4]. See also Bedford [6].
We introduce boundary special generic maps, a class of submersions from manifolds with boundary to Euclidean spaces whose restriction to the boundary has only boundary definite fold points as its singular points. We derive the…
We extend the concept of eigenvector centrality to multiplex networks, and introduce several alternative parameters that quantify the importance of nodes in a multi-layered networked system, including the definition of vectorial-type…
One of the ways that connectedness has been studied through the history of topology is by using chains, the so called chain connectedness. Here we combine this notion together with continuity up to a covering to provide the inheritance of…
We present a surprisingly new connection between two well-studied combinatorial classes: rooted connected chord diagrams on one hand, and rooted bridgeless combinatorial maps on the other hand. We describe a bijection between these two…
In this note for a topological group $G$, we introduce a bounded subset of $G$ and we find some relationships of this definition with other topological properties of $G$.
The dominated convergence theorem implies that if (f_n) is a sequence of functions on a probability space taking values in the interval [0,1], and (f_n) converges pointwise a.e., then the sequence of integrals converges to the integral of…
In this note we establish some connections between the theory of self-similar fractals in the sense of John E. Hutchinson (cf. [3]) and the theory of boundary quotients of $C^\ast$-algebras associated to monoids. Although we must leave…
On the one hand, we provide the first examples of arbitrarily highly connected (compact) bad orbifolds. On the other hand, we show that n-connected n-orbifolds are manifolds. The latter improves the best previously known bound of Lytchak by…
We study problems related to continuous boundary extension of mappings of Orlicz-Sobolev classes in terms of prime ends. The results we obtain concern the case when the mappings are open, discrete, but not closed (not preserving the…
This note studies a network of agents having continuous-time dynamics with quantized interactions and time-varying directed topology. Due to the discontinuity of the dynamics, solutions of the resulting ODE system are intended in the sense…
For nonmonotonic logics, Cumulativity is an important rule. We show here that Cumulativity fans out into an infinity of different conditions, if the domain is not closed under finite unions.