一般拓扑

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显示 2025年08月07日， 星期四 新的列表

新提交 (展示 2 之 2 条目 )

[1] arXiv:2508.04029 [中文pdf, pdf, html, 其他]

标题： 一种有效的网络拓扑压缩进化过程 显示英文标题

标题： An Evolution Process for Effective Network Topological Compression

Jian-Hui Li, Zu-Guo Yu, Yu-Chu Tian

评论： 15页，10图

主题： 一般拓扑 (math.GN)

网络动态为理解复杂系统的行为和演化提供了关键见解。 在此，我们关注网络的拓扑动态，以探索一种减少平均距离的独特过程：拓扑压缩。 压缩过程本质上涉及一系列网络拓扑变换，通常可以通过重连技术实现。 本文提出了一种实现有效网络拓扑压缩的进化机制，并在各种合成网络上实验验证了其性能。 这些结果在网络拓扑压缩动力学领域建立了一个范例。 显示英文摘要

Network dynamics offers critical insights into the behavior and evolution of complex systems. Here, we focus on the topological dynamics of networks to explore a unique process for reducing the average distance: topological compression. The compression process essentially involves a series of network topological transformations, which can generally be achieved through rewiring technique. This paper proposes an evolutionary mechanism for achieving effective network topological compression and experimentally validates its performance across various synthetic networks. These results establish a paradigm in the field of network topological compression dynamics.

[2] arXiv:2508.04328 [中文pdf, pdf, html, 其他]

标题： 距离泛函在重度量下的一致收敛性和超空间拓扑的下确界 显示英文标题

标题： Uniform convergence of distance functionals under remetrization and infima of hyperspace topologies

Yogesh Agarwal, Varun Jindal

评论： 25页

主题： 一般拓扑 (math.GN)

The objective of this paper is twofold. In the first half of the paper, we investigate upper parts of the hyperspace convergences determined by uniform convergence of distance functionals on a bornology under different metrizations of a metrizable space. To do this, a new covering property associated with the underlying bornology is introduced. An independent study of this new covering notion in relation to some well-known notions, such as strong uniform continuity, is also presented. In the second half, we study the infima of hyperspace convergences (induced by distance functionals) determined by a family of (uniformly) equivalent metrics. In particular, we establish the existence of the minimum element for the collection of upper Attouch-Wets convergences corresponding to all equivalent metrics on a metrizable space $X$. We show that such a minimum element exists if and only if $X$ has a compatible Heine-Borel metric. Our findings give several new insights into the theory of hyperspace convergences. 显示英文摘要

The objective of this paper is twofold. In the first half of the paper, we investigate upper parts of the hyperspace convergences determined by uniform convergence of distance functionals on a bornology under different metrizations of a metrizable space. To do this, a new covering property associated with the underlying bornology is introduced. An independent study of this new covering notion in relation to some well-known notions, such as strong uniform continuity, is also presented. In the second half, we study the infima of hyperspace convergences (induced by distance functionals) determined by a family of (uniformly) equivalent metrics. In particular, we establish the existence of the minimum element for the collection of upper Attouch-Wets convergences corresponding to all equivalent metrics on a metrizable space $X$. We show that such a minimum element exists if and only if $X$ has a compatible Heine-Borel metric. Our findings give several new insights into the theory of hyperspace convergences.

交叉提交 (展示 1 之 1 条目 )

[3] arXiv:2508.04168 (交叉列表自 math.RT) [中文pdf, pdf, html, 其他]

标题： 关于多虚拟辫群 $M_kVB_n$ 和多焊接辫群 $M_kWB_n$的表示 显示英文标题

标题： On representations of the multi-virtual braid group $M_kVB_n$ and the multi-welded braid group $M_kWB_n$

Vaibhav Keshari, Mohamad N. Nasser, Madeti Prabhakar

主题： 表示理论 (math.RT) ; 一般拓扑 (math.GN)

本文将多重虚拟辫群$M_kVB_n$的复数齐性$2$-局部表示分类为$\mathrm{GL}_n(\mathbb{C})$对$n\geq3$和$k >1$，表明这样的表示正好分为$2^{k+1}+1$种不同的类型，其中除了三种以外都是不忠实的。 此外，本文研究了多重焊接辫群 $M_kWB_n$ 到 $\mathrm{GL}_n(\mathbb{C})$ 的复数齐次 $2$-局部表示，对于 $n\geq3$ 和 $k >1$，确定了 $3 \cdot 2^{k-1} +1$ 表示。 此外，文章包含了一个非局部表示的构造，即$M_2WB_3$，它扩展了已知的辫群在$3$根弦上的LKB表示，即$B_3$，为一般构造$M_kWB_n$的非局部表示指明了一条路径。 显示英文摘要

This paper classifies complex homogeneous $2$-local representations of the multiple virtual braid group $M_kVB_n$ into $\mathrm{GL}_n(\mathbb{C})$ for $n\geq3$ and $k >1$, showing that such representations fall into exactly $2^{k+1}+1$ distinct types, out of which except three all are unfaithful. In addition, this paper investigates complex homogeneous $2$-local representations of the multiple welded braid group $M_kWB_n$ into $\mathrm{GL}_n(\mathbb{C})$ for $n\geq3$ and $k >1$, identifying $3 \cdot 2^{k-1} +1$ representations. Moreover, the article includes a construction of a non-local representation of $M_2WB_3$ that extends the known LKB representation of the braid group on $3$ strands, namely $B_3$, making a path towards constructing non-local representations of $M_kWB_n$ in general.

替换提交 (展示 1 之 1 条目 )

[4] arXiv:2409.15569 (替换) [中文pdf, pdf, html, 其他]

标题： 序列足以进行无点均匀完成 显示英文标题

标题： Sequences suffice for pointfree uniform completions

Graham Manuell

评论： 17页，小修改

主题： 一般拓扑 (math.GN)

度量空间的补全通常使用柯西序列来构造。 然而，这在一般的统一空间中不适用，必须改用柯西滤子或网。 而在无点拓扑学中情况更简单：统一局部的正确补全确实可以作为柯西序列局部的商得到。 显示英文摘要

Completions of metric spaces are usually constructed using Cauchy sequences. However, this does not work for general uniform spaces, where Cauchy filters or nets must be used instead. The situation in pointfree topology is more straightforward: the correct completion of uniform locales can indeed be obtained as a quotient of a locale of Cauchy sequences.