Topology and its Applications最新文献

英文中文

Flip graph and arc complex finite rigidity 翻转图和弧复有限刚度

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2026-01-13 DOI: 10.1016/j.topol.2026.109729

Chandrika Sadanand, Emily Shinkle

A subcomplex

X

of a cell complex

C

is called rigid with respect to another cell complex

C^{'}

if every injective simplicial map

λ : X \to C^{'}

has a unique extension to an injective simplicial map

ϕ : C \to C^{'}

. We say that a cell complex exhibits finite rigidity if it contains a finite, rigid subcomplex. Given a surface with marked points, its flip graph and arc complex are simplicial complexes indexing the triangulations and the arcs between marked points, respectively. In this paper, we leverage the fact that the flip graph can be embedded in the arc complex as its dual to show that finite rigidity of the flip graph implies finite rigidity of the arc complex. Thus, a recent result of the second author on the finite rigidity of the flip graph implies finite rigidity of the arc complex for a broad class of surfaces. Notably, this includes surfaces with boundary – a setting where finite rigidity of the arc complex was previously unknown. We further show that these arc complexes admit exhaustions by finite rigid sets, which was shown to be an important component in the proof of many interesting model-theoretic properties of simplicial complexes associated to surfaces in a recent work of de la Nuez Gonzalez-Disarlo-Koberda.

如果每个单射简单映射λ:X→C ‘对单射简单映射φ:C→C ’有唯一的扩展，则胞复合体C的子复合体X相对于另一个胞复合体C '是刚性的。如果一个细胞复合体包含一个有限的刚性子复合体，我们就说它具有有限刚性。给定一个有标记点的曲面，其翻转图和弧复形分别是标记三角形和标记点之间的弧的简单复形。在本文中，我们利用翻转图可以嵌入弧复合体作为其对偶的事实来证明翻转图的有限刚性意味着弧复合体的有限刚性。因此，第二作者最近关于翻转图的有限刚性的结果暗示了弧复合体对于广泛的曲面类的有限刚性。值得注意的是，这包括有边界的表面，在这种情况下，弧复合体的有限刚度以前是未知的。在de la Nuez gonzalez - disarro - koberda最近的一篇文章中，我们进一步证明了这些弧复合体允许有限刚性集的耗尽，这在证明与曲面相关的简单复合体的许多有趣的模型论性质中是一个重要的组成部分。

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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 : 2026-01-13 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

A note on the local base at closed subsets in GO-spaces go空间闭子集上局部基的一个注释

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2026-01-12 DOI: 10.1016/j.topol.2026.109728

Yu-Ming Deng, Liang-Xue Peng

In this note, we prove that every GO-space is s-

m_{1}

, which gives an affirmative answer to Lin's question [5, Question 3.1] and Peng's question [6, Question 3.4]. In the last part of this note, we point out that there is a gap in Theorem 3.3 in [6] but the statement of the theorem is correct because in this paper we have established a stronger fact in Theorem 3.4.

在本文中，我们证明了每个go空间都是s-m1，这对Lin的问题[5，问题3.1]和Peng的问题[6，问题3.4]给出了肯定的答案。在这篇笔记的最后一部分，我们指出在[6]中定理3.3有一个空白，但定理的陈述是正确的，因为在本文中我们在定理3.4中建立了一个更强的事实。

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 : 2026-01-12 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

On a variation of selective separability using ideals 用理想论选择性可分性的变化

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2026-01-09 DOI: 10.1016/j.topol.2026.109725

Debraj Chandra , Nur Alam , Dipika Roy

A space X is H-separable (Bella et al. (2009) [6]) if for every sequence

(Y_{n} : n \in N)

of dense subspaces of X there exists a sequence

(F_{n} : n \in N)

such that for each n

F_{n}

is a finite subset of

Y_{n}

and every nonempty open set of X intersects

F_{n}

for all but finitely many n. In this paper, we introduce and study an ideal variant of H-separability, called

I

-H-separability.

如果对于X的密集子空间的每一个序列（Yn:n∈n）存在一个序列（Fn:n∈n），使得对于每一个n Fn是Yn的有限子集，并且X的每一个非空开集除有限多个n外都与Fn相交，则空间X是h可分的（Bella et al.(2009)[6]）。本文引入并研究了h可分性的一个理想变体，称为i - h可分性。

引用次数: 0

Submetrizability in quotient spaces of semitopological groups 半拓扑群商空间中的可子化性

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2026-01-08 DOI: 10.1016/j.topol.2026.109724

Xuewei Ling

In this paper, we investigate submetrizability in quotient spaces of semitopological groups. The following results are obtained: (1) If H is a closed neutral subgroup of a semitopological group G such that

G / H

is a Hausdorff paracompact space with

H s_{l} (G / H) \cdot ψ (G / H) \leq ω

, then

G / H

is submetrizable; (2) If H is a closed neutral subgroup of a semitopological group G such that

G / H

is Hausdorff (resp., Tychonoff) and

H s_{l} (G / H) \cdot I n_{l} (G / H) \cdot ψ (G / H) \leq ω

, then

G / H

admits a continuous bijection onto a Hausdorff space with a countable base (resp., admits a weaker separable metrizable topology).

本文研究了半拓扑群商空间中的子可化性。得到以下结果：(1)如果H是半拓扑群G的闭中立子群，使得G/H是一个Hsl(G/H)⋅ψ(G/H)≤ω的Hausdorff准紧空间，则G/H是可子化的；(2)若H是半拓扑群G的闭中性子群，使得G/H为Hausdorff （resp.）， Tychonoff)和Hsl(G/H)⋅Inl(G/H)⋅ψ(G/H)≤ω，则G/H允许一个连续双射到具有可数基的Hausdorff空间上。，承认一个较弱的可分可度量拓扑)。

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 : 2026-01-02 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

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2026-01-01

引用次数: 0

On the structure of the hyperspace of convergent sequences of ordinal numbers 收敛序数序列的超空间结构

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2025-12-31 DOI: 10.1016/j.topol.2025.109708

Yasser F. Ortiz-Castillo

In this paper we study the hyperspace of nontrivial convergent sequences of ordinal spaces. We prove that

ω^{ω}

characterizes all hyperspaces

S_{c} ([0, α))

for

ω < α \leq 2 ω

. Also we improve a result from [4] by showing that

S_{c} ([0, α))

has the Baire property for every

α > ω

. Finally we show that the closure of

S_{c} ([0, α))

K ([0, α))

is a zero dimensional compactification of

S_{c} ([0, α))

which differs from its Stone-Čech compactification.

本文研究了有序空间的非平凡收敛序列的超空间。证明了ωω刻画了ω<；α≤2ω下的所有超空间Sc([0,α))。我们还改进了[4]的一个结果，证明Sc([0,α))对每个α>；ω都具有贝尔性质。最后证明Sc（[0,α))在K（[0,α)）中的闭包是Sc([0,α)）的零维紧化，不同于它的Stone-Čech紧化。

引用次数: 0

Countability in quotient spaces of sequential topological groups 序拓扑群商空间中的可数性

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2025-12-23 DOI: 10.1016/j.topol.2025.109705

Bin Zhao, Jiewen Chen, Xuewei Ling

In this article, quotient spaces of sequential topological groups are investigated. The following results are obtained: (1) Let H be a closed subgroup of a sequential topological group G, then

G / H

is an

α_{4}

-space ⇔

G / H

is Fréchet-Urysohn ⇔

G / H

is strongly Fréchet-Urysohn, which gives a partial answer to [27, Question 3.9]; (2) Let H be a closed neutral subgroup of a sequential topological group G, then

G / H

is metrizable ⇔

G / H

is feathered and csf-countable, which gives a partial answer to [26, Question 1.10]; (3) Some characterizations of countability in quotient spaces of sequential topological groups.

本文研究了序拓扑群的商空间。得到了以下结果：(1)设H是序拓扑群G的闭子群，则G/H是α4空间；⇔G/H是fr切特-乌里松；(2)设H是序拓扑群G的闭中立子群，则G/H是可度量的⇔G/H是带羽的，csf可数，给出了[26，问题1.10]的部分答案；(3)序拓扑群商空间中可数性的若干刻画。

引用次数: 0

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