软C连续性和软几乎C连续性之间的软拓空间
1Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid 22110, Jordan.
Heliyon
|June 2, 2023
概括
这项研究引入了软连续性的较弱形式,称为软c连续性和软近c连续性. 这些新概念的特性和应用在软拓空间的软紧密性特征的探索.
科学领域:
- 拓学的拓学
- 集合理论 集合理论
- 数学分析的数学分析
背景情况:
- 软拓学的现有研究集中在软连续性和软几乎连续性等概念上.
- 需要这些概念的较弱形式来提供软拓空间的更细致的分析.
- 在拓学研究中,了解受限制和构成下的函数的行为至关重要.
研究的目的:
- 引入和定义软c连续性和软近c连续性作为现有的软拓概念的较弱版本.
- 研究这些新概念在软限制下的表征,属性和保存.
- 探索表现出这些新连续性类型的函数的组成及其对软紧性的影响.
主要方法:
- 开发软c连续性和软近c连续性的理论框架.
- 利用软限制来分析这些新的连续性类型的行为.
- 采用软开放集和软正则开放集来表征软紧性和软基.
- 研究软连续函数的组成.
- 将新的软拓概念与它们的一般拓类型进行比较.
主要成果:
- 已经建立了软c连续性和软近c连续性的几种表征.
- 这些新的连续性概念被证明可以在软限制下保持.
- 确定软c连续函数和软近c连续函数的组合条件.
- 提供了使用软 - 开放集的软紧性的特征.
- 软正则开放集的集合与软紧的补充被证明是形成一个柔软的基础,一个粗的软拓.
结论:
- 该研究成功地引入并分析了软拓学中新型较弱的连续性形式.
- 这些发现有助于更深入地了解软拓空间,特别是关于紧性和功能组成.
- 这项研究突出了软拓与一般拓之间的关系,弥合了理论上的差距.
相关概念视频
01:12Equation of Continuity
8.5K
Fluid motion is represented by either velocity vectors or streamlines. The volume of a fluid flowing past a given location through an area during a period of time is called the flow rate Q, or more precisely, the volume flow rate. Flow rate and velocity are related—for instance, a river has a greater flow rate if the velocity of the water in it is greater. However, the flow rate also depends on the size and shape of the river. The relationship between flow rate (Q) and average speed (v)...
8.5K
01:34Woodward–Hoffmann Selection Rules and Microscopic Reversibility
3.2K
Electrocyclic reactions, cycloadditions, and sigmatropic rearrangements are concerted pericyclic reactions that proceed via a cyclic transition state. These reactions are stereospecific and regioselective. The stereochemistry of the products depends on the symmetry characteristics of the interacting orbitals and the reaction conditions. Accordingly, pericyclic reactions are classified as either symmetry-allowed or symmetry-forbidden. Woodward and Hoffmann presented the selection criteria for...
3.2K
01:20Region of Convergence of Laplace Tarnsform
614
The Region of Convergence (ROC) is a fundamental concept in signal processing and system analysis, particularly associated with the Laplace transform. The ROC represents an area in the complex plane where the Laplace transform of a given signal converges, determining the transform's applicability and utility.
Consider a decaying exponential signal that begins at a specific time. When deriving its Laplace transform, the time-domain variable is replaced with a complex variable. This...
Consider a decaying exponential signal that begins at a specific time. When deriving its Laplace transform, the time-domain variable is replaced with a complex variable. This...
614
01:21Boundary Conditions: Lossless Lines
124
Consider a single-phase, two-wire, lossless transmission line terminated by an impedance at the receiving end and a source with Thevenin voltage and impedance at the sending end. The line, with length, has a surge impedance and wave velocity determined by the line's inductance and capacitance.
At the receiving end, the boundary condition states that the voltage equals the product of the receiving-end impedance and current. This relationship is expressed as a function of the incident and...
At the receiving end, the boundary condition states that the voltage equals the product of the receiving-end impedance and current. This relationship is expressed as a function of the incident and...
124
01:06Divergence and Stokes' Theorems
1.7K
The divergence and Stokes' theorems are a variation of Green's theorem in a higher dimension. They are also a generalization of the fundamental theorem of calculus. The divergence theorem and Stokes' theorem are in a way similar to each other; The divergence theorem relates to the dot product of a vector, while Stokes' theorem relates to the curl of a vector. Many applications in physics and engineering make use of the divergence and Stokes' theorems, enabling us to write...
1.7K
01:15Routh-Hurwitz Criterion I
291
Consider an electrical power grid, where stability is essential to prevent blackouts. The Routh-Hurwitz criterion is a valuable tool for assessing system stability under varying load conditions or faults. By analyzing the closed-loop transfer function, the Routh-Hurwitz criterion helps determine whether the system remains stable.
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
291