Topology and its Applications最新文献

英文中文

Arcs, circles, finite graphs and inverse limits of set-valued functions on intervals 弧，圆，有限图和集值函数在区间上的逆极限

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2026-03-01 Epub Date: 2026-01-14 DOI: 10.1016/j.topol.2026.109711

Sina Greenwood , Michael Lockyer

In this paper we investigate conditions for an inverse limit of set-valued functions on intervals to be a graph, and in particular an arc or a circle. We analyse how ramification points are formed and give a characterisation of the order of a point in an inverse limit of set-valued functions that is a finite graph, and we strengthen a result by Nall and Vidal-Escobar who showed that if an inverse limit of set-valued functions on intervals is a finite graph, then it is homeomorphic to the Mahavier product of the first n functions of the sequence for some

n \in N

. Recently the notion of a splitting sequence was introduced to provide a characterisation of inverse limits on intervals that are arcs. We survey necessary conditions for a set-valued inverse limit to be an arc or circle which includes a generalisation of this notion.

本文研究了区间上集值函数的逆极限是图，特别是弧或圆的条件。我们分析了分支点是如何形成的，给出了集值函数的反极限是有限图的一个点的阶的刻画，并加强了Nall和Vidal-Escobar的结论，即如果区间上的集值函数的反极限是有限图，那么对于某n∈n，它与序列的前n个函数的Mahavier积是同纯的。最近，分裂序列的概念被引入，以提供弧区间逆极限的表征。我们研究了集值逆极限是弧或圆的必要条件，其中包含了这一概念的推广。

引用次数: 0

G-movability and large subgroups g -可动性和大亚群

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2026-03-01 Epub Date: 2026-01-13 DOI: 10.1016/j.topol.2026.109731

Hugo Juárez-Anguiano , Raúl Juárez-Flores

In this paper, we prove the following result: Let H be a closed subgroup of a compact metrizable group G. Then

G / H

is G-movable if and only if H is a large subgroup of G. It provides a new characterization of large subgroups and generalizes a result of Gevorgyan [12] about compact Lie groups.

本文证明了以下结果：设H是紧可测度群G的一个闭子群，则G/H是G可动的当且仅当H是G的一个大子群，给出了大子群的一个新的表征，推广了关于紧李群的Gevorgyan[12]的一个结果。

引用次数: 0

Round twin groups on few strands 在几股上圆的孪生群

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2026-03-01 Epub Date: 2026-01-13 DOI: 10.1016/j.topol.2026.109727

Jacob Mostovoy

We study the space

Q_{n}

of all configurations of n ordered points on the circle such that no three points coincide, and in which one of the points (say, the last one) is fixed. We compute its fundamental group for

n < 6

and describe its homology for

n = 6, 7

. For arbitrary n, we compute its first homology and its Euler characteristic.

We use three geometric approaches. On one hand,

Q_{n}

is naturally defined as the complement of an arrangement of codimension-2 subtori in a real torus. On the other hand,

Q_{n}

is homotopy equivalent to an explicit nonpositively curved cubical complex. Finally,

Q_{n}

can also be assembled from no-3-equal manifolds of the real line.

We also observe that, up to homotopy,

Q_{n}

may be identified with a subspace of the oriented double cover of the moduli space

{\overline{M}}_{0, n} (R)

of stable real rational curves with n marked points. This gives an embedding of

π_{1} Q_{n}

into the pure cactus group. As a corollary, we see that

π_{1} Q_{n}

is residually nilpotent.

我们研究了圆上n个有序点的所有构型的空间Qn，使得没有三个点重合，并且其中一个点（比如最后一个点）是固定的。我们计算了n<；6的基群，并描述了n=6,7的同调。对于任意n，我们计算了它的第一同调和欧拉特性。我们使用三种几何方法。一方面，Qn自然地被定义为实环面中余维-2子环面排列的补。另一方面，Qn是同伦等价于显非正弯曲的立方复形。最后，Qn也可以由实线的no-3等流形组合而成。我们还观察到，在同伦以内，Qn可以被识别为具有n个标记点的稳定实有理曲线的模空间M的0，n(R)的有向双盖的一个子空间。这使得π1Qn嵌入到纯仙人掌群中。作为推论，我们看到π1Qn是剩余幂零的。

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引用次数: 0

Bridging graph-theoretical and topological approaches: Connectivity and Jordan curves in the digital plane 桥接图理论和拓扑方法：数字平面上的连通性和约旦曲线

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2026-03-01 Epub Date: 2026-01-14 DOI: 10.1016/j.topol.2026.109730

Yazmin Cote, Carlos Uzcátegui-Aylwin

This article explores the connections between graph-theoretical and topological approaches in the study of the Jordan curve theorem for grids. Building on the foundational work of Rosenfeld, who developed adjacency-based concepts on

Z^{2}

, and the subsequent introduction of the topological digital plane

K^{2}

with the Khalimsky topology by Khalimsky, Kopperman, and Meyer, we investigate the interplay between these perspectives. Inspired by the work of Khalimsky, Kopperman, and Meyer, we define an operator

Γ^{⁎}

transforming subsets of

Z^{2}

into subsets of

K^{2}

. This operator is essential for demonstrating how 8-paths, 4-connectivity, and other discrete structures in

Z^{2}

correspond to topological properties in

K^{2}

. Moreover, we address whether the topological Jordan curve theorem for

K^{2}

can be derived from the graph-theoretical version on

Z^{2}

. Our results illustrate the deep and intricate relationship between these two methodologies, shedding light on their complementary roles in digital topology.

本文探讨了图论方法和拓扑方法在研究网格约旦曲线定理中的联系。Rosenfeld在Z2上开发了基于邻接的概念，随后由Khalimsky、Kopperman和Meyer引入了拓扑数字平面K2与Khalimsky拓扑，在此基础上，我们研究了这些观点之间的相互作用。受Khalimsky， Kopperman和Meyer工作的启发，我们定义了一个算子Γ 将Z2的子集转换为K2的子集。这个算子对于演示Z2中的8路、4连通性和其他离散结构如何对应于K2中的拓扑性质是必不可少的。此外，我们讨论了K2的拓扑Jordan曲线定理是否可以由Z2的图论版本导出。我们的结果说明了这两种方法之间深刻而复杂的关系，揭示了它们在数字拓扑中的互补作用。

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引用次数: 0

Extending quasi-alternating links III 扩展拟交替连杆III

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2026-03-01 Epub Date: 2026-01-16 DOI: 10.1016/j.topol.2026.109736

Kirandeep Kaur , Nafaa Chbili

Champanerkar and Kofman [1] introduced a method for constructing quasi-alternating links by replacing a quasi-alternating crossing in a link diagram with a rational tangle of the same type. This approach, however, does not generally extend to alternating tangles of the opposite type or to non-alternating tangles.

In this paper, we identify sufficient conditions under which the construction remains valid when the crossing is replaced by an alternating rational tangle of opposite type. We also prove that this method applies to certain non-alternating pretzel tangles. As an application, we provide a table of non-alternating quasi-alternating knots with 13 crossings obtained using this construction. Additionally, we describe an infinite family of quasi-alternating links featuring a non-twisted quasi-alternating crossing that satisfies these sufficient conditions.

Champanerkar和Kofman等人提出了一种构造准交替链路的方法，即用同类型的有理缠结代替链路图中的准交替交叉。然而，这种方法通常不适用于相反类型的交替缠结或非交替缠结。在本文中，我们确定了当交叉被相反类型的交替理性缠结取代时结构仍然有效的充分条件。我们还证明了该方法适用于某些非交替的椒盐卷饼缠结。作为应用，我们给出了用这种构造得到的具有13个交点的非交变准交变结表。此外，我们还描述了满足这些充分条件的具有非扭曲拟交变交叉的无限族拟交变链路。

引用次数: 0

On limit sets and equicontinuity in the hyperspace of continua in dimension one 一维连续超空间的极限集与等连续

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2026-03-01 Epub Date: 2025-12-10 DOI: 10.1016/j.topol.2025.109690

Domagoj Jelić , Piotr Oprocha

The paper studies the structure of ω-limit sets of map

\tilde{f}

induced on the hyperspace

C (G)

of all connected compact sets, by dynamical system

(G, f)

acting on a topological graph G. In the case of the base space being a topological tree we additionally show that

\tilde{f}

is always almost equicontinuous and characterize its Birkhoff center.

本文研究了由作用于拓扑图G的动力系统（G,f）在所有连通紧集的超空间C(G)上导出的映射f ~的ω-极限集的结构。在基空间为拓扑树的情况下，我们进一步证明了f ~总是几乎等连续的，并刻画了它的Birkhoff中心。

引用次数: 0

Diagonals of separately pointwise Lipschitz functions of n variables 有n个变量的单点Lipschitz函数的对角线

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2026-03-01 Epub Date: 2026-01-12 DOI: 10.1016/j.topol.2026.109726

Olena Karlova , Volodymyr Mykhaylyuk

We study the diagonals

g (x) = f (x, \dots, x)

of (strongly) separately Lipschitz mappings

f : X^{n} \to Y

. It is shown that for any metric space X and any normed space Y the diagonals of strongly separately pointwise Lipschitz mappings

f : X^{n} \to Y

are exactly stable limits of sequences of pointwise Lipschitz mappings (a mapping on the product of n metric spaces is strongly separately pointwise Lipschitz if it is jointly pointwise Lipschitz mapping with respect to any

n - 1

variables). We introduce classes

{PL}_{n} (X, Y)

of mappings between metric spaces X and Y which are recursively defined from pointwise Lipschitz mappings, analogously as mappings of stable Baire classes are recursively defined from continuous mappings. It was shown that

f \in {PL}_{n} (X, Y)

for a metric space X and a Banach space Y if and only if there exists a sequence

{(X_{k})}_{k = 1}^{\infty}

of ambiguous sets

X_{k} \subseteq X

of the class n such that every restriction

f |_{X_{k}}

is Lipschitz. Moreover, for any metric space X, any normed space Y and every

n \geq 2

we construct a separately pointwise Lipschitz mapping

f : X^{n} \to Y

with given diagonal

g \in {PL}_{n - 1} (X, Y)

分别研究了（强）Lipschitz映射f:Xn→Y的对角线g(x)=f（x，…，x）。证明了对于任意度量空间X和任意赋范空间Y，强分别点向Lipschitz映射f:Xn→Y的对角线正是点向Lipschitz映射序列的稳定极限（n个度量空间积上的映射如果是对任意n−1个变量的联合点向Lipschitz映射，则是强分别点向Lipschitz映射）。引入由点向Lipschitz映射递归定义的度量空间X和Y之间映射的类PLn(X，Y)，类似于由连续映射递归定义稳定Baire类的映射。证明了对于度量空间X和Banach空间Y， f∈PLn（X，Y）当且仅当存在n类的二义集合Xk⊥X的一个序列（Xk）k=1∞，使得|Xk的每一个限制都是Lipschitz。此外，对于任意度量空间X、任意赋范空间Y和任意n≥2，我们分别构造了一个给定对角线g∈PLn−1（X，Y）的点向Lipschitz映射f:Xn→Y。

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引用次数: 0

Meshed continua have unique n-fold symmetric product suspension 网格连续体具有独特的n次对称积悬

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2026-03-01 Epub Date: 2025-12-23 DOI: 10.1016/j.topol.2025.109706

Felipe de J. Aguilar-Romero, David Herrera-Carrasco, Fernando Macías-Romero

Let X be a metric continuum, and let n be a positive integer. We denote by

F_{n} (X)

the hyperspace consisting of all nonempty closed subsets of X with at most n points. For

n > 1

, the n-fold symmetric product suspension of X is the quotient space

F_{n} (X) / F_{1} (X)

. In this paper, we prove that if X is a meshed continuum,

n \geq 4

, and Y is a continuum such that

F_{n} (X) / F_{1} (X)

is homeomorphic to

F_{n} (Y) / F_{1} (Y)

, then X is homeomorphic to Y.

设X是度规连续统，n是正整数。我们用Fn(X)表示由X的所有非空闭子集组成的超空间，这些子集最多有n个点。对于n>；1， X的n次对称积悬是商空间Fn(X)/F1(X)。本文证明了如果X是网格连续体，n≥4，且Y是Fn(X)/F1(X)同胚于Fn(Y)/F1(Y)的连续体，则X同胚于Y。

引用次数: 0

Nonlocal loss of first homotopy in polyhedral approximations of Peano continua Peano连续体多面体近似中第一同伦的非局部损失

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2026-03-01 Epub Date: 2026-01-02 DOI: 10.1016/j.topol.2025.109710

Jeremy Brazas , Hanspeter Fischer

If a Peano continuum X is semilocally simply connected, then it has a finite polyhedral approximation whose fundamental group is isomorphic to that of X. In general, this fails to be true. It is known that the fundamental group of a locally complicated Peano continuum may contain nontrivial elements that are persistently undetectable by polyhedral approximations, at all scales. However, we show that such failure is not inherently local.

如果一个Peano连续体X是半局部单连通的，那么它有一个有限多面体近似，其基本群与X同构。一般来说，这是不成立的。众所周知，局部复杂的皮亚诺连续统的基本群可能包含在所有尺度上多面体近似持续检测不到的非平凡元素。然而，我们表明这种失败并不是固有的局部的。

引用次数: 0

Cardinal invariants of a meager ideal 贫乏理想的基数不变量

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2026-02-15 Epub Date: 2025-07-07 DOI: 10.1016/j.topol.2025.109516

Will Brian

Let

M_{X}

denote the ideal of meager subsets of a topological space X. We prove that if X is a completely metrizable space without isolated points, then the smallest cardinality of a non-meager subset of X, denoted

non (M_{X})

, is exactly

non (M_{X}) = cf {[κ]}^{ω} \cdot non (M_{R})

, where κ is the minimum weight of a nonempty open subset of X. We also characterize the additivity and covering numbers for

M_{X}

in terms of simple topological properties of X. Some bounds are proved and some questions raised concerning the cofinality of

M_{X}

and the cofinality of the related ideal of nowhere dense subsets of X.

We also show that if X is a compact Hausdorff space with π-weight κ, then

non (M_{X}) \leq cf {[κ]}^{ω} \cdot non (M_{R})

. This bound for compact Hausdorff spaces is not sharp, in the sense that it is consistent for such a space to have non-meager subsets of even smaller cardinality.

我们证明了如果X是一个没有孤立点的完全可度量空间，那么X的一个非贫乏子集的最小基数，记为non(MX)，正好是non(MX)=cf[κ]ω⋅non(MR)，其中，κ是X的一个非空开子集的最小权值。我们还用X的简单拓扑性质刻画了MX的可加性和覆盖数。我们证明了MX的一些界，并提出了关于MX的协性和X的无密集子集的相关理想的协性的一些问题。我们还证明了如果X是一个π权κ的紧Hausdorff空间，则non(MX)≤cf[κ]ω⋅non（MR）。紧化Hausdorff空间的这个界并不尖锐，因为这样的空间具有更小基数的非贫乏子集是一致的。

{"title":"Cardinal invariants of a meager ideal","authors":"Will Brian","doi":"10.1016/j.topol.2025.109516","DOIUrl":"10.1016/j.topol.2025.109516","url":null,"abstract":"<div><div>Let <math><msub><mrow><mi>M</mi></mrow><mrow><mi>X</mi></mrow></msub></math> denote the ideal of meager subsets of a topological space X. We prove that if X is a completely metrizable space without isolated points, then the smallest cardinality of a non-meager subset of X, denoted <math><mrow><mi>non</mi></mrow><mo>(</mo><msub><mrow><mi>M</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>)</mo></math>, is exactly <math><mrow><mi>non</mi></mrow><mo>(</mo><msub><mrow><mi>M</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>)</mo><mo>=</mo><mrow><mi>cf</mi></mrow><msup><mrow><mo>[</mo><mi>κ</mi><mo>]</mo></mrow><mrow><mi>ω</mi></mrow></msup><mo>⋅</mo><mrow><mi>non</mi></mrow><mo>(</mo><msub><mrow><mi>M</mi></mrow><mrow><mi>R</mi></mrow></msub><mo>)</mo></math>, where κ is the minimum weight of a nonempty open subset of X. We also characterize the additivity and covering numbers for <math><msub><mrow><mi>M</mi></mrow><mrow><mi>X</mi></mrow></msub></math> in terms of simple topological properties of X. Some bounds are proved and some questions raised concerning the cofinality of <math><msub><mrow><mi>M</mi></mrow><mrow><mi>X</mi></mrow></msub></math> and the cofinality of the related ideal of nowhere dense subsets of X.</div><div>We also show that if X is a compact Hausdorff space with π-weight κ, then <math><mrow><mi>non</mi></mrow><mo>(</mo><msub><mrow><mi>M</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>)</mo><mo>≤</mo><mrow><mi>cf</mi></mrow><msup><mrow><mo>[</mo><mi>κ</mi><mo>]</mo></mrow><mrow><mi>ω</mi></mrow></msup><mo>⋅</mo><mrow><mi>non</mi></mrow><mo>(</mo><msub><mrow><mi>M</mi></mrow><mrow><mi>R</mi></mrow></msub><mo>)</mo></math>. This bound for compact Hausdorff spaces is not sharp, in the sense that it is consistent for such a space to have non-meager subsets of even smaller cardinality.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"379 ","pages":"Article 109516"},"PeriodicalIF":0.5,"publicationDate":"2026-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145948065","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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