Topology and its Applications最新文献

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An upper bound for the number of critical points of the systole function on the moduli space of hyperbolic surfaces 双曲面模空间上收缩函数临界点数量的上界

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2024-10-17 DOI: 10.1016/j.topol.2024.109091

Yue Gao

We obtain an upper bound for the number of critical points of the systole function on

M_{g}

. Besides, we obtain an upper bound for the number of those critical points whose systole is smaller than a constant.

我们得到了 Mg 上收缩函数临界点数量的上限。此外，我们还得到了收缩率小于常数的临界点的数量上限。

引用次数: 0

Degenerations of the product geometries in projective space that contain Nil 包含 Nil 的投影空间积几何的退化

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2024-10-15 DOI: 10.1016/j.topol.2024.109078

Thomas Shifley , Steve Trettel

This paper produces explicit conjugacy paths for the product geometries

H^{2} \times R

and

S^{2} \times R

whose limits contain the geometry of the Heisenberg group's action on itself. These are the first such conjugacy limits to any model of Nil, continuing the program of Daryl Cooper, Jeffrey Danciger, and Anna Wienhard to determine all possible degenerations between Thurston geometries in

(PGL (4, R), {RP}^{3})

本文为乘积几何 H2×R 和 S2×R 提出了明确的共轭路径，其极限包含海森堡群作用于自身的几何。这是任何 Nil 模型的第一个此类共轭极限，延续了 Daryl Cooper、Jeffrey Danciger 和 Anna Wienhard 的计划，即确定 (PGL(4,R),RP3) 中 Thurston 几何图形之间所有可能的退化。

引用次数: 0

Hattori subspaces 服部子空间

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2024-10-15 DOI: 10.1016/j.topol.2024.109077

Angel Calderón-Villalobos , Iván Sánchez

For a subset A of an almost topological group

(G, τ)

, the Hattori space

H (A)

is a topological space whose underlying set is G and whose topology

τ (A)

is defined as follows: if

x \in A

(respectively,

x \notin A

), then the neighborhoods of x in

H (A)

are the same neighborhoods of x in the reflection group

(G_{⁎}, τ_{⁎})

(respectively,

(G, τ)

). Given an infinite subset X of an almost topological group G and

A \subseteq X

, we denote by

X (A)

X_{⁎}

and X to the spaces

(X, τ (A) |_{X})

(X, τ_{⁎} |_{X})

and

(X, τ |_{X})

, respectively. We say that

X (A)

is the Hattori subspace associated to A. In this paper, we obtain information about Hattori subspaces. We show that some known topological spaces can be obtained as Hattori subspaces of some almost topological groups.

对于一个几乎拓扑群（G,τ）的子集 A，服部空间 H(A) 是一个拓扑空间，其底层集是 G，其拓扑 τ(A) 的定义如下：如果 x∈A（分别为 x∉A），那么 x 在 H(A) 中的邻域就是 x 在反射群（G⁎,τ⁎）（分别为 (G,τ)）中的邻域。给定几乎拓扑群 G 的无限子集 X 和 A⊆X，我们分别用 X(A)、X⁎ 和 X 表示空间 (X,τ(A)|X)、(X,τ⁎|X) 和 (X,τ|X)。我们说 X(A) 是与 A 相关联的服部子空间。我们证明，一些已知的拓扑空间可以作为一些近似拓扑群的服部子空间得到。

引用次数: 0

Velichko's notions close to sequential separability and their hereditary variants in Cp-theory 维利奇科的接近于顺序可分性的概念及其在 Cp 理论中的遗传变异

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2024-10-02 DOI: 10.1016/j.topol.2024.109076

Alexander V. Osipov

A space X is sequentially separable if there is a countable

S \subset X

such that every point of X is the limit of a sequence of points from S. In 2004, N.V. Velichko defined and investigated concepts close to sequential separability: σ-separability and F-separability. The aim of this paper is to study σ-separability and F-separability (and their hereditary variants) of the space

C_{p} (X)

of all real-valued continuous functions, defined on a Tychonoff space X, endowed with the pointwise convergence topology. In particular, we proved that σ-separability coincides with sequential separability. Hereditary variants (hereditarily σ-separability and hereditarily F-separability) coincide with Fréchet–Urysohn property in the class of cosmic spaces.

如果存在一个可数 S⊂X，使得 X 的每个点都是来自 S 的点序列的极限，则空间 X 是顺序可分的。2004 年，N.V. Velichko 定义并研究了与顺序可分性接近的概念：σ 可分性和 F 可分性。本文的目的是研究所有实值连续函数空间 Cp(X) 的 σ 可分性和 F 可分性（及其遗传变异），这些函数定义在泰克诺夫空间 X 上，并赋有点收敛拓扑。我们特别证明了 σ 可分性与顺序可分性重合。在宇宙空间类中，遗传变异（遗传σ可分性和遗传F可分性）与弗雷谢特-乌里索恩性质重合。

引用次数: 0

A complete invariant for shift equivalence for Boolean matrices and finite relations 布尔矩阵和有限关系的移位等价完全不变式

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2024-10-02 DOI: 10.1016/j.topol.2024.109075

Ethan Akin , Marian Mrozek , Mateusz Przybylski , Jim Wiseman

We give a complete invariant for shift equivalence for Boolean matrices (equivalently finite relations), in terms of the period, the induced partial order on recurrent components, and the cohomology class of the relation on those components.

我们给出了布尔矩阵（等价于有限关系）移动等价性的完整不变式，即周期、循环成分上的诱导偏序以及这些成分上关系的同调类。

引用次数: 0

On diagonal degrees and star networks 关于对角线度和星形网络

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2024-10-01 DOI: 10.1016/j.topol.2024.109074

Nathan Carlson

Given an open cover

U

of a topological space X, we introduce the notion of a star network for

U

. The associated cardinal function

s n (X)

, where

e (X) \leq s n (X) \leq L (X)

, is used to establish new cardinal inequalities involving diagonal degrees. We show

| X | \leq s n {(X)}^{Δ (X)}

for a

T_{1}

space X, giving a partial answer to a long-standing question of Angelo Bella. Many further results are given using variations of

s n (X)

. One result has as corollaries Buzyakova's theorem that a ccc space with a regular

G_{δ}

-diagonal has cardinality at most

c

, as well as three results of Gotchev. Further results lead to logical improvements of theorems of Basile, Bella, and Ridderbos, a partial solution to a question of the same authors, and a theorem of Gotchev, Tkachenko, and Tkachuk. Finally, we define the Urysohn extent

U e (X)

with the property

U e (X) \leq \min {a L (X), e (X)}

and use the Erdős-Rado theorem to show that

| X | \leq 2^{U e (X) \overline{Δ} (X)}

for any Urysohn space X.

给定拓扑空间 X 的开盖 U，我们引入 U 的星形网络概念。相关的心形函数 sn(X)（其中 e(X)≤sn(X)≤L(X) ）用于建立涉及对角度的新心形不等式。我们证明了 T1 空间 X 的 |X|≤sn(X)Δ(X)，部分回答了安杰洛-贝拉（Angelo Bella）的一个长期问题。利用 sn(X) 的变化给出了许多进一步的结果。其中一个结果的推论是布扎科娃（Buzyakova）的定理，即具有规则 Gδ 对角线的ccc 空间的心性至多为 c，以及哥切夫（Gotchev）的三个结果。进一步的结果导致了巴西尔、贝拉和里德博斯定理的逻辑改进，同一作者的一个问题的部分解答，以及哥切夫、特卡琴科和特卡丘克的一个定理。最后，我们定义了具有 Ue(X)≤min{aL(X),e(X)} 特性的乌里索恩程度 Ue(X)，并使用厄尔多斯-拉多定理证明了对于任何乌里索恩空间 X，|X|≤2Ue(X)Δ‾(X)。

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引用次数: 0

Approximations by disjoint subcontinua and indecomposability 不相邻子连续体的逼近和不可分解性

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2024-09-27 DOI: 10.1016/j.topol.2024.109071

David S. Lipham

We study approximations of continuum-wise connected spaces, or semicontinua, and show that every indecomposable semicontinuum can be approximated from within by a sequence of pairwise disjoint continua. As a corollary, we find that if X is a G-like continuum or a one-dimensional non-separating plane continuum, which is the closure of an indecomposable semicontinuum, then X is indecomposable. We also prove that a composant of an indecomposable continuum cannot be embedded into a Suslinian continuum.

我们研究了连续面连接空间或半连续面的近似，并证明每个不可分解的半连续面都可以从内部被一连串成对相离的连续面近似。作为推论，我们发现如果 X 是类 G 连续体或一维非分离平面连续体（即不可分解半连续体的闭包），那么 X 是不可分解的。我们还证明了不可分解连续统的合成子不能嵌入到苏斯林连续统中。

引用次数: 0

Calculation of Nielsen periodic numbers on infra-solvmanifolds 下溶漫游体上尼尔森周期数的计算

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2024-09-19 DOI: 10.1016/j.topol.2024.109073

Changbok Li

Recently, a formula for computing the Nielsen periodic numbers

N F_{n} (f)

and

N P_{n} (f)

of self maps f on infra-nilmanifolds and infra-solvmanifolds of type (R) was found. In this paper, we extend this formula to the case of general infra-solvmanifolds. We show that infra-solvmanifolds are essentially reducible to the GCD and essentially toral, and determine conditions under which

N F_{n} (f) = N (f^{n})

. We show that the prime Nielsen-Jiang periodic number

N P_{n} (f)

of a self map f on an infra-solvmanifold M can be calculated by Nielsen numbers of lifts of suitable iterates of f to an

NR

-solvmanifold that finitely covers M.

最近，我们发现了一个公式，用于计算下零曼形和下溶曼形上自映射 f 的尼尔森周期数 NFn(f) 和 NPn(f)。在本文中，我们将这一公式推广到一般的下溶点。我们证明了下溶漫游体本质上可还原为 GCD，本质上是环状的，并确定了 NFn(f)=N(fn) 的条件。我们证明了下溶漫性 M 上自映射 f 的素数尼尔森-蒋周期数 NPn(f) 可以通过 f 向有限覆盖 M 的 NR 溶漫性的合适迭代的提升的尼尔森数来计算。

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引用次数: 0

Hereditarily decomposable continua have non-block points 可遗传分解连续体具有非块点

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2024-09-16 DOI: 10.1016/j.topol.2024.109072

Daron Anderson

In this note we expand upon our results from [1] to show that every nondegenerate hereditarily decomposable Hausdorff continuum has two or more non-block points, i.e. points whose complements contain a continuum-connected dense subset. The celebrated non-cut point existence theorem states that all nondegenerate Hausdorff continua have two or more non-cut points, and the corresponding result for non-block points is known to hold for metrizable continua. It is also known that there are consistent examples of Hausdorff continua with no non-block points, but that non-block point existence holds for Hausdorff continua that are either aposyndetic, irreducible, or separable.

在本注释中，我们扩展了[1]中的结果，证明每个非enerate 遗传可分解豪斯多夫连续体都有两个或两个以上的非块点，即其补集包含连续体连接密集子集的点。著名的非切点存在定理指出，所有非enerate Hausdorff 连续体都有两个或两个以上的非切点。人们还知道，有一些豪斯多夫连续体的一致例子不存在非块点，但非块点的存在对于无块、不可还原或可分离的豪斯多夫连续体是成立的。

引用次数: 0

The Jones polynomial for a torus knot with twists 带捻环结的琼斯多项式

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2024-09-11 DOI: 10.1016/j.topol.2024.109069

Brandon Bavier , Brandy Doleshal

We compute the Jones polynomial for a three-parameter family of links, the twisted torus links of the form $T ((p, q), (2, s))$ where p and q are coprime and s is nonzero. When $s = 2 n$ , these links are the twisted torus knots $T (p, q; 2, n)$ . We show that for $T (p, q; 2, n)$ , the Jones polynomial is trivial if and only if the knot is trivial.

我们计算了一个三参数链节族的琼斯多项式，即 T((p,q),(2,s))形式的扭曲环链节，其中 p 和 q 是共素数，s 是非零。当 s=2n 时，这些链接就是扭曲环结 T(p,q;2,n)。我们将证明，对于 T(p,q;2,n)，如果且只有当结是琐碎的，琼斯多项式才是琐碎的。

引用次数: 0

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