Topology and its Applications最新文献

英文中文

The bounded topology 有界拓扑

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.2025.109517

Fernando Hernández-Hernández , Michael Hrušák , Norberto Javier Rivas-González

We introduce a topology on ideals stronger than the usual metric topology as a means for coarse classification of ideals. We study its properties and relation to the combinatorial properties of the ideals. This topology generalizes the submeasure topology on analytic P-ideals introduced by S. Solecki. We give a partial answer to a conjecture of A. Louveau and B. Veličković.

我们引入了一种比通常度量拓扑更强的理想拓扑，作为理想粗分类的一种手段。研究了它的性质及其与理想组合性质的关系。这种拓扑推广了S. Solecki在解析p理想上引入的子测度拓扑。我们对a . Louveau和B. veli kovovic的一个猜想给出了部分的回答。

引用次数: 0

Guest editorial and preface for the special issue celebrating the 80th birthday of Istvan Juhasz 为庆祝伊斯特万·尤哈兹80岁生日特刊的客座社论和序言

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2026-02-15 Epub Date: 2025-07-04 DOI: 10.1016/j.topol.2025.109499

Alan Dow (Guest Editor), Lajos Soukup (Guest Editor), Bill Weiss (Guest Editor)

引用次数: 0

Function spaces and points in Čech-Stone remainders Čech-Stone余数中的函数空间和点

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2026-02-15 Epub Date: 2025-07-04 DOI: 10.1016/j.topol.2025.109501

Jan Baars , Jan van Mill

Let X and Y be locally compact normal spaces and let

u \in X^{⁎}

and

v \in Y^{⁎}

. In this paper we will show that if

X_{u}

and

Y_{v}

are

l_{p}

-equivalent then u is ω-near if and only if v is. This result does not necessarily hold for spaces that are not locally compact. We will also show for locally compact normal spaces X and Y, that if

u \in X^{⁎}

and

v \in Y^{⁎}

are ω-near and

X_{u}

and

Y_{v}

are

l_{p}

-equivalent, then

ω_{\hat{u}}

and

ω_{\hat{v}}

are homeomorphic for some ‘unique’

\hat{u}, \hat{v} \in ω^{⁎}

‘good’ for u and v. These results allow us to find an isomorphic classification of function spaces

C_{p} (α_{u})

, where

α < ω^{ω}

is a limit ordinal and

u \in α^{⁎}

. This extends a result due to Gul'ko for

α = ω

. We will also indicate that the proof for this isomorphic classification can only partly be extended for

α \geq ω^{ω}

设X和Y是局部紧正规空间，设u∈X， v∈Y。在本文中，我们将证明如果Xu和Yv是lp等价的，那么当且仅当v是ω-时，u是ω-附近的。这个结果并不一定适用于非局部紧化的空间。我们还将证明对于局部紧正规空间X和Y，如果u∈X和v∈Y是ω-近的，Xu和Yv是lp等价的，则ωu和ωv对于某些‘唯一’的u是同纯的，v∈ω对u和v ‘好’。这些结果允许我们找到函数空间Cp（αu）的一个同构分类，其中α<；ωω是一个极限序数，u∈α。这是对α=ω时古尔科定理的推广。我们还将指出，对于α≥ω，这个同构分类的证明只能部分地推广。

引用次数: 0

On the ABK conjecture, alpha-well quasi orders and Dress-Schiffels product 关于ABK猜想、准序和Dress-Schiffels积

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2026-02-15 Epub Date: 2025-07-04 DOI: 10.1016/j.topol.2025.109502

Uri Abraham , Robert Bonnet , Maurice Pouzet

The following is a 2008 conjecture from [3]

[ABK Conjecture] Every well quasi order (wqo) is a countable union of better quasi orders (bqo).

We obtain some partial progress on the conjecture, in that we show that the class of orders that are a countable union of better quasi orders (sigma-bqo) is closed under various operations. These include diverse products, such as the little known but natural Dress-Shieffels product. We develop various properties of the latter. In relation with the main question, we explore the class of alpha-wqo for countable ordinals alpha and obtain several closure properties and a Hausdorff-style classification theorem. Our main contribution is the discovery of various properties of sigma-bqos and ruling out potential counterexamples to the ABK Conjecture.

下面是[3]在2008年的一个猜想[ABK猜想]。每一个好的拟序（wqo）是一个好的拟序（bqo）的可数并。我们在这个猜想上取得了一些部分进展，证明了在各种操作下，较优拟序的可数并的阶类（sigma-bqo）是闭的。这些产品包括各种各样的产品，比如鲜为人知但天然的Dress-Shieffels产品。我们发展了后者的各种性质。针对主要问题，我们探讨了可数序数α的α -wqo类，得到了几个闭包性质和一个hausdorff式分类定理。我们的主要贡献是发现了sigma-bqos的各种性质，并排除了ABK猜想的潜在反例。

引用次数: 0

Generic selective independent families 一般选择性独立家族

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2026-02-15 Epub Date: 2025-07-04 DOI: 10.1016/j.topol.2025.109504

Vera Fischer, Corey Bacal Switzer

We prove that the generic maximal independent family obtained by iteratively forcing with the Mathias forcing relative to diagonalization filters is densely maximal. Moreover, by choosing the filters with some care one can ensure the family is selective and hence forcing indestructible in a strong sense. Using this we prove that under

p = 2^{ℵ_{0}}

there are selective independent families and also we show how to add selective independent families of any desired size.

我们证明了用Mathias强迫相对于对角化滤波器的迭代强迫得到的一般极大独立族是密集极大的。此外，通过仔细选择过滤器，可以确保家庭是有选择性的，从而在强烈的意义上强迫坚不可摧。利用这一方法，我们证明了在p=2 ~ 0条件下存在选择性独立族，并展示了如何添加任意大小的选择性独立族。

引用次数: 0

An example distinguishing two convex sequential properties 一个区分两个凸序列性质的例子

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2026-02-15 Epub Date: 2025-07-05 DOI: 10.1016/j.topol.2025.109511

Christina Brech

Corson and Efremov introduced convex notions of countable tightness and the Fréchet-Urysohn property in the context of Banach spaces. We present an old unpublished example which consistently distinguishes these properties. Together with a recent result from [12], it yields that it is independent from ZFC whether these properties are equivalent or not.

Corson和Efremov在Banach空间中引入了可数紧性的凸概念和fr - urysohn性质。我们提出一个旧的未发表的例子，一致区分这些属性。结合[12]最近的一个结果，它得出了这些性质是否等价与ZFC无关。

引用次数: 0

Concentrated sets and γ-sets in the Miller model Miller模型中的集中集和γ集

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.2025.109503

Valentin Haberl , Piotr Szewczak , Lyubomyr Zdomskyy

Using combinatorial covering properties, we show that there is no concentrated set of reals of size

ω_{2}

in the Miller model. The main result refutes a conjecture of Bartoszyński and Halbeisen. We also prove that there are no γ-set of reals of size

ω_{2}

in the Miller model.

利用组合覆盖性质，我们证明了在Miller模型中不存在大小为ω2的实数的集中集。主要结果驳斥了Bartoszyński和Halbeisen的一个猜想。我们还证明了在Miller模型中不存在大小为ω2的实数γ集。

引用次数: 0

Game extensions of floppy graph metrics 游戏扩展软盘图形指标

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.2025.109515

Taras Banakh , Pietro Majer

<div><div>A graph metric on a set X is any function <math><mi>d</mi><mo>:</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>d</mi></mrow></msub><mo>→</mo><msub><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msub><mo>≔</mo><mo>{</mo><mi>x</mi><mo>∈</mo><mi>R</mi><mo>:</mo><mi>x</mi><mo>></mo><mn>0</mn><mo>}</mo></math> defined on a connected graph <math><msub><mrow><mi>E</mi></mrow><mrow><mi>d</mi></mrow></msub><mo>⊆</mo><msup><mrow><mo>[</mo><mi>X</mi><mo>]</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>≔</mo><mo>{</mo><mi>A</mi><mo>⊆</mo><mi>X</mi><mo>:</mo><mo>|</mo><mi>A</mi><mo>|</mo><mo>=</mo><mn>2</mn><mo>}</mo></math> and such that for every edge <math><mo>{</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>}</mo><mo>∈</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>d</mi></mrow></msub></math> we have <math><mi>d</mi><mo>(</mo><mo>{</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>}</mo><mo>)</mo><mo>≤</mo><mover><mrow><mi>d</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>≔</mo><mi>inf</mi><mo>⁡</mo><mo>{</mo><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>n</mi></mrow></msubsup><mi>d</mi><mo>(</mo><mo>{</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>}</mo><mo>)</mo><mo>:</mo><mo>{</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>}</mo><mo>=</mo><mo>{</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>}</mo><mspace></mspace><mo>∧</mo><mspace></mspace><mo>{</mo><mo>{</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>}</mo><mo>:</mo><mn>0</mn><mo><</mo><mi>i</mi><mo>≤</mo><mi>n</mi><mo>}</mo><mo>⊆</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>d</mi></mrow></msub><mo>}</mo></math>. A graph metric <math><mi>d</mi><mo>:</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>d</mi></mrow></msub><mo>→</mo><msub><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msub></math> is called a full metric on X if <math><msub><mrow><mi>E</mi></mrow><mrow><mi>d</mi></mrow></msub><mo>=</mo><msup><mrow><mo>[</mo><mi>X</mi><mo>]</mo></mrow><mrow><mn>2</mn></mrow></msup></math>. A graph metric <math><mi>d</mi><mo>:</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>d</mi></mrow></msub><mo>→</mo><msub><mrow><mover><mrow><mi>R</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>+</mo></mrow></msub></math> is floppy if <math><mover><mrow><mi>d</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>></mo><mover><mrow><mi>d</mi></mrow><mrow><mo>ˇ</mo></mrow></mover><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>≔</mo><mi>sup</mi><mo>⁡</mo><mo>{</mo><mi>d</m

集合X上的图度量是在连通图Ed (X) 2上定义的任意函数d:Ed→R+是{X∈R: X >；0}的对象，其中包括{A， X:|A|=2}，并且对于每个边{X，y}∈Ed，我们有d({X,y})≤d, （X,y}）的对象是inf(∑i=1) ({xi−1,xi}):{X,y}={x0,xn}∧{{xi−1,xi}:0<i≤n}。图度规d:Ed→R+称为X上的满度规，如果Ed=[X]2。图指标d: Ed→R¯+软盘如果dˆ(x, y)在dˇ(x, y)≔一口⁡{d ({A, b})−dˆ(A, x)−dˆ(b, y): {A、b}∈Ed}每x, y∈x {x, y}∉Ed。证明了对于集合X上任意软盘图度量d:Ed→R+，点X， y∈X∈{X, y} Ed，实数R∈13d′(X, y)+23d′(X, y)≤r<d′（X, y），函数d∪{< {X, y}, R >}是一个软盘图度量。这意味着对于具有可数集[X]2∈Ed的每一个软盘图度量d:Ed→R+，以及对于R+的密集子集的每一个索引族（Fe）e∈[X]2∈Ed，存在一个内射函数R∈∏e∈[X]2∈EdFe，使得d∪R是一个满度量。同时，我们证明了后一个结果不能推广到不可数集合上的部分度量。

引用次数: 0

A counterexample related to a theorem of Komjáth and Weiss 一个与Komjáth和Weiss定理有关的反例

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2026-02-15 Epub Date: 2025-07-03 DOI: 10.1016/j.topol.2025.109505

Rodrigo Carvalho, Assaf Rinot

In a paper from 1987, Komjáth and Weiss proved that for every regular topological space X of character less than

b

, if

X \to {(top ω + 1)}_{ω}^{1}

, then

X \to {(top α)}_{ω}^{1}

for all

α < ω_{1}

. In addition, assuming ⋄, they constructed a space X of size continuum, of character

b

, satisfying

X \to {(top ω + 1)}_{ω}^{1}

, but not

X \to {(top ω^{2} + 1)}_{ω}^{1}

. Here, a counterexample space with the same characteristics is obtained outright in

ZFC

在1987年的一篇论文中，Komjáth和Weiss证明了对于每一个小于b的正则拓扑空间X，如果X→(topω+1)ω1，那么对于所有α<；ω1, X→(topα)ω1。此外，在假设条件下，他们构造了一个尺寸为连续体的空间X，其特征为b，满足X→(topω+1)ω1，但不满足X→(topω2+1)ω1。这里，在ZFC中直接得到了一个具有相同特征的反例空间。

引用次数: 0

Chain version of some cardinal inequalities 一些基本不等式的链式形式

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2026-02-15 Epub Date: 2025-07-03 DOI: 10.1016/j.topol.2025.109508

Angelo Bella

Combining results of Balogh and Juhász, we improve a chain version of Arhangel'skiĭ-Šapirovskiĭ's inequality. This is done by replacing the Lindelöf degree with the linear Lindelöf degree. Then, we consider the almost discretely Lindelöf degree.

结合Balogh和Juhász的结果，我们改进了Arhangel’ski’-Šapirovskiĭ不等式的链式版本。这是通过将Lindelöf度替换为线性的Lindelöf度来完成的。然后，我们考虑几乎离散的Lindelöf度。

引用次数: 0

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