Topology and its Applications最新文献

英文中文

A nonsymmetric approach to coincidences of admissible multi-valued maps 可容许多值映射重合的非对称方法

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2025-11-24 DOI: 10.1016/j.topol.2025.109670

Allan Edley Ramos de Andrade , Northon Canevari Leme Penteado , Sergio Tsuyoshi Ura

Given G a finite group which acts on

S^{n}

and H a normal cyclic subgroup of prime order, in [1] the authors have defined and estimated the cohomological dimension of the set

A_{φ} (F, H, G)

(H, G)

-coincidence points of an acyclic multi-valued map

F : X ⊸ Y

relative to an essential map

φ : X \to S^{n}

, where X is a compact Hausdorff space and Y is a k-dimensional CW-complex. In this work we extended this result to an admissible multi-valued map

F : X ⊸ Y

and to an essential multi-valued map

Φ : X ⊸ S^{n}

such that

T^{i} (Φ (x)) \cap Φ (x) = \emptyset, i = 1, \dots, p

. Furthermore, we define and estimate the cohomological dimension of a coincidence set

A (F, Φ)

where

F : X ⊸ M

Φ : X ⊸ N

are two admissible multi-valued maps and N is a connected closed manifold and a homology n-sphere.

给定G是作用于Sn的有限群，H是素阶的正规循环子群，在[1]中定义并估计了非循环多值映射F:X X→Sn的（H，G）-重合点的集合a φ（F，H，G）相对于本质映射φ:X→Sn的上同调维数，其中X是紧Hausdorff空间，Y是k维cw复形。在本工作中，我们将此结果推广到一个容许多值映射F:X X Y和一个本质多值映射Φ：X X Sn，使得Ti（Φ(X)）∩Φ(X)=∅,i=1，…，p。进一步，我们定义并估计了重合集a （F，Φ）的上同调维数，其中F:X × M， Φ：X × N是两个可容许的多值映射，N是连通闭流形和同调N球。

引用次数: 0

From λ-hollow frames to λ-repletions in W: III. Continuous convergence in RL W: III从λ空心框架到λ填充。RL中的连续收敛

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2025-11-20 DOI: 10.1016/j.topol.2025.109667

Richard N. Ball , Anthony W. Hager , Joanne Walters-Wayland

We show that classical continuous convergence has an elegant and powerful formulation in

R L

, the W-object of real functions on the locale L. Here W is the category of divisible archimedean ℓ-groups with designated weak order units, and cW is the category of W-objects equipped with a suitable convergence structure, together with the continuous W-homomorphisms. We exhibit an adjunction between the functor

R_{c}

, which assigns to the locale L the cW-object

R L

equipped with its continuous convergence, and its left adjoint

K_{c}

, which assigns to a given cW-object its frame of cW-kernels, i.e., its frame of convergence closed W-kernels. A significant attribute of the adjunction is that its unit is the Cauchy completion.

The suitable convergences, here termed admissible W-convergences, include the classical convergences, are Hausdorff, and are all coarser than relative uniform convergence and finer than α-convergence. (Pointfree pointwise convergence, however, is not admissible.) We show that the coarse admissible convergences on a W-object G are in bijective correspondence with the dense nuclei on the frame

K G

of W-kernels of G. Finally, we show that the κ-closure nucleus on

K G

, i.e., the closure of the W-kernels of G under κ-joins, corresponds to the coarse admissible W-convergence on G whose Cauchy completion is the κ-repletion of G.

我们证明了经典连续收敛在RL中有一个优雅而有力的表述，即l上实数函数的W-对象。这里W是具有指定弱阶单位的可分阿基姆群的范畴，cW是具有合适收敛结构的W-对象的范畴，以及连续W同态。我们展示了函子Rc和它的左伴子Kc之间的一个共轭，前者赋予区域L一个连续收敛的cw -对象RL，后者赋予给定的cw -对象一个cw -核的框架，即它的收敛闭w核的框架。附加的一个重要属性是它的单位是柯西补全。适当的收敛，这里称为可容许的w收敛，包括经典收敛，是Hausdorff收敛，都比相对一致收敛粗，比α-收敛细。（然而，无点的逐点收敛是不允许的。）证明了w -对象G上的粗容许收敛与G的w -核的框架KG上的密核是双射对应的，最后证明了KG上的κ-闭核，即G的w -核在κ-连接下的闭，对应于G上的粗容许w -收敛，其柯西补全是G的κ-填充。

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引用次数: 0

On the Morava K-theory of the real Grassmannian Gr3(Rm) 论实格拉斯曼Gr3（Rm）的Morava k理论

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2025-11-19 DOI: 10.1016/j.topol.2025.109665

Phan Hoàng Chơn , Nguyễn Đặng Hồ Hải

N. Kuhn and C. Lloyd conjectured in [8] that the rank of the mod-2 Morava K-theory

K {(n)}^{⁎}

of the real Grassmannian manifolds

G r_{d} (R^{m})

could be written as a sum of products of binomial coefficients. The conjecture is easy for

d = 1

and was already checked by Kuhn and Lloyd for

d = 2

. The aim of this paper is to check this conjecture for the case

d = 3

n . Kuhn和C. Lloyd在[8]中推测，实格拉斯曼流形的mod2 Morava K-理论K(n)的秩可以写成二项式系数积的和。这个猜想在d=1时很容易，在d=2时已经被Kuhn和Lloyd验证过了。本文的目的是在d=3的情况下检验这个猜想。

引用次数: 0

N-expansiveness of generic surface diffeomorphisms 一般曲面微分同态的n -可扩展性

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2025-11-17 DOI: 10.1016/j.topol.2025.109664

Ziteng Ma

We prove that a

C^{1}

generic diffeomorphism of a closed surface is N-expansive for some positive integer N if and only if it is Anosov. Consequently, every closed surface different from the torus exhibits a residual subset of

C^{1}

diffeomorphisms, none of which is N-expansive. This contrasts with a result of Artigue [2].

证明了对于正整数N，闭曲面的C1泛微分同构是可扩展的，当且仅当它是Anosov。因此，每个不同于环面的封闭曲面都有C1个微分同态的残差子集，其中没有一个是可扩展的。这与阿蒂格的结果形成了对比。

引用次数: 0

Quasi covering dimension of topological spaces 拓扑空间的拟覆盖维数

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2025-11-14 DOI: 10.1016/j.topol.2025.109661

Chunxu Ji , Kaiyun Wang

This paper focuses on the quasi covering dimension of topological spaces. We prove that a topological space and its Kolmogorov quotient space have the same quasi covering dimension. Subsequently, for a finite

T_{0}

space

(X, τ)

, we show that its quasi covering dimension

d i m_{q} (X, τ) = \max {w i d t h (↓ x) | x \in Max (X)} - 1

, where

Max (X)

is the set of all maximal elements of X under the specialization order. Furthermore, we investigate the subspace theorems of quasi covering dimension of finite topological spaces and give an example presenting that the Cartesian product theorem does not hold in general. Finally, we discuss the relationships between the quasi covering dimension of topological spaces and that of frames.

本文主要研究拓扑空间的拟覆盖维数。证明了拓扑空间及其Kolmogorov商空间具有相同的拟覆盖维数。随后，对于有限T0空间（X,τ），我们证明了其拟覆盖维dimq(X,τ)=max (width（↓X） | X∈max (X)}−1，其中max (X)是X在专门化阶下所有极大元素的集合。进一步研究了有限拓扑空间中拟覆盖维数的子空间定理，并给出了笛卡尔积定理不成立的一个例子。最后，讨论了拓扑空间的拟覆盖维数与框架的拟覆盖维数之间的关系。

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引用次数: 0

Any countable product of ordinals is dually discrete 序数的任何可数积都是对偶离散的

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2025-11-13 DOI: 10.1016/j.topol.2025.109662

Zhengbo Fang, Lei Mou

In this paper, we mainly prove that any countable product of ordinals is dually discrete. To get the result, we use the method which is called reverse induction by Patrakeev in [5].

本文主要证明了序数的可数积是对偶离散的。为了得到结果，我们使用了Patrakeev在[5]中称为反向诱导的方法。

引用次数: 0

Strong asymptotically nonexpansive action and common fixed points on weak and weak⁎ compact convex sets 弱和弱紧凑凸集上的强渐近非扩张作用和公共不动点

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2025-11-13 DOI: 10.1016/j.topol.2025.109663

Abhishek

In 1971, R. D. Holmes and A. T.-M. Lau generalized the class of nonexpansive action by introducing the notion of asymptotically nonexpansive action of a semitopological semigroup S on a nonempty subset K of a Banach space U. They proved that a right reversible asymptotically nonexpansive action of a semitopological semigroup S on C has a common fixed point in C whenever C is a nonempty compact convex set having the property (B) in a Banach space U. In 2018, Aminpour et al. introduced the notion of strong asymptotically nonexpansive action of a semitopological semigroup S on a nonempty subset K of a Banach space U. Aminpour et al. gave an analogous result to R. D. Holmes and A. T.-M. Lau without the property (B). Without the assumption of property (B), we prove that a left reversible strong asymptotically nonexpansive action of a semitopological semigroup S on W has a common fixed point in W whenever W is a nonempty weakly compact convex set in a uniformly convex in every direction Banach space U. Moreover, it is proved that a strong asymptotically nonexpansive action of a semitopological semigroup S on W has a common fixed point in W whenever W is a nonempty weakly compact convex set having the normal structure in a Banach space U and S is compact and reversible. Under the assumption of the asymptotic center property, it is proved that a strong asymptotically nonexpansive action of a commutative semitopological semigroup S on E has a common fixed point in E whenever E is a nonempty weak^⁎ compact convex set in a dual Banach space

U^{⁎}

1971年，r·d·霍姆斯和a·t·m。Lau通过引入半拓扑半群S在Banach空间u的非空子集K上的渐近非扩张作用的概念，推广了非扩张作用的类别。他们证明了当C是Banach空间u中具有(B)性质的非空紧凸集时，半拓扑半群S在C上的右可逆渐近非扩张作用在C上有一个公共不动点。引入半拓扑半群S在Banach空间的非空子集K上的强渐近非扩张作用的概念。没有财产的法律(B)。在不假设性质(B)的情况下，证明了半拓扑半群S在W上的左可逆强渐近非扩张作用在W上有一个公共不动点，只要W是Banach空间u各方向上的一致凸上的非空弱紧凸集。证明了当W是Banach空间U中具有正规结构的非空弱紧致凸集，且S紧致可逆时，半拓扑半群S对W的强渐近非扩张作用在W上有一个公共不动点。在渐近中心性质的假设下，证明了交换半拓扑半群S对E的强渐近非扩张作用在E中有一个公共不动点，当E是对偶Banach空间U中一个非空弱紧凑凸集时。

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引用次数: 0

On fundamental groups of spaces of framed embeddings of a circle in a 4-manifold 关于4流形中圆的框架嵌入空间的基本群

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2025-11-11 DOI: 10.1016/j.topol.2025.109658

Danica Kosanović

Motivated by recent results on diffeomorphisms of 4-manifolds, this paper investigates fundamental groups of spaces of embeddings of

S^{1} \times D^{3}

in 4-manifolds. The majority of work goes into the case of framed immersed circles.

在最近关于4流形的微分同态的研究结果的启发下，本文研究了4流形中S1×D3嵌入空间的基本群。大部分工作都是在框架浸入式圆的情况下进行的。

引用次数: 0

Transitivity of some uniformities on fuzzy sets 模糊集上一些一致性的传递性

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2025-11-10 DOI: 10.1016/j.topol.2025.109660

Daniel Jardón , Iván Sánchez , Manuel Sanchis

Given a uniform space

(X, U)

, we denote by

F (X)

the family of all normal upper semicontinuous fuzzy sets

u : X \to [0, 1]

with compact support. In this paper, we study transitivity on some uniformities on

F (X)

: the level-wise uniformity

U_{\infty}

, the Skorokhod uniformity

U_{0}

, and the sendograph uniformity

U_{S}

. If

f : (X, U) \to (X, U)

is a continuous function, we mainly characterize when the induced dynamical systems

\hat{f} : (F (X), U_{\infty}) \to (F (X), U_{\infty})

\hat{f} : (F (X), U_{0}) \to (F (X), U_{0})

and

\hat{f} : (F (X), U_{S}) \to (F (X), U_{S})

are transitive, where

\hat{f}

is the Zadeh's extension of f.

给定一个一致空间（X，U），用F(X)表示具有紧支持的所有正规上半连续模糊集U:X→[0,1]的族。本文研究了F(X)上一些均匀性的可传递性：水平均匀性U∞、Skorokhod均匀性U0和传感器均匀性US。如果f:（X，U）→（X，U）是连续函数，我们主要刻画了f:（f (X),U∞）→（f (X),U∞）、f:（f (X),U0）→（f (X),U0）和f:（f (X)，US）→（f （X)，US）是可传递的，其中f: f (X)，US）→（f (X)，US）是f的Zadeh扩展。

引用次数: 0

On deformation spaces, tangent groupoids and generalized filtrations of Banach and Fredholm manifolds Banach和Fredholm流形的变形空间、切线群和广义滤波

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2025-11-10 DOI: 10.1016/j.topol.2025.109659

Ahmad Reza Haj Saeedi Sadegh, Jody Trout

We extend the deformation to the normal cone and tangent groupoid constructions from finite-dimensional manifolds to infinite-dimensional Banach and Fredholm manifolds. Next, we generalize the concept of Fredholm filtrations to get a more flexible and functorial theory. In particular, we show that if M is a Banach (or Fredholm) manifold with generalized filtration

F = {M_{n}}_{1}^{\infty}

by finite-dimensional submanifolds, then there are induced generalized filtrations

T F = {T M_{n}}_{1}^{\infty}

of the tangent bundle TM and

T F = {T M_{n}}_{1}^{\infty}

of the tangent groupoid

T M

, which is not possible in the classical theory.

我们将变形扩展到从有限维流形到无限维Banach和Fredholm流形的正锥和切线群形结构。其次，我们推广了Fredholm滤波的概念，得到了一个更灵活的泛函理论。特别地，我们证明了如果M是由有限维子流形进行广义滤波F={Mn}1∞的Banach（或Fredholm）流形，则存在切束TM的归纳广义滤波TF={TMn}1∞和切群样TM的归纳广义滤波TF={TMn}1∞，这在经典理论中是不可能的。

引用次数: 0

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