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An ideal on a set X is a nonempty collection of subsets of X closed under the operations of subset (heredity) and finite unions (additivity). Given a topological space (X,τ) an ideal ℐ on X and A⊆X, ψ(A) is defined as ⋃{U∈τ:U−A∈ℐ}. A topology, denoted τ*,
T. R. Hamlett, David Rose
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A Study on Topological Space for an Ideal Topological Space
An ideal topological space is a triplet (X, τ, ℑ), where X is a nonempty set, τ is a topology on X, and ℑ is an ideal of subsets of X. In this paper, we introduce L∗-perfect, R∗-perfect, and C∗-perfect sets in ideal spaces and study their properties. We obtained a characterization for compatible ideals via R∗-perfect sets. Also, we obtain a generalized
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A dynamic interfacial semi‐interpenetrating polymer network is constructed by sequential assembly of β‐sheet‐rich SF and CS‐RL. The SF framework provides mechanical strength, while dynamically associated CS‐RL enables local rearrangement, allowing droplets to rapidly reconfigure without loss of interfacial integrity.
Yaping Zhang +7 more
wiley +1 more source
A generalization of m-topology and U-topology on rings of measurable functions
In this paper, we generalize mμ and Uμ topologies on M ( X , A ) via an ideal I in the ring M ( X , A ) of all real-valued measurable functions. The collection LI∞ ( μ ) of all essentially I-bounded functions over the measure space (X,A,μ)$ and the ...
Soumyadip Acharyya +3 more
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Properties of I-submaximal ideal topological spaces
In [2], the notion of I-submaximal ideal topological spaces is introduced and studied. In this paper, several characterizations and further properties of I -submaximal ideal topological spaces are obtained.
EKİCİ, ERDAL, Noiri, Takashi
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Engineered red blood cell‐derived extracellular vesicles (eRBCEVs) are synthesized via controlled microfluidic assembly from native RBC lipids, enabling tunable encapsulation of proteins, nucleic acids, nanoparticles, and viral vectors. The platform demonstrates reproducible nanoscale architecture, preserved membrane composition, and functional cargo ...
Chiranth K. Nagaraj +23 more
wiley +1 more source
Neutrosophic Nano ideal topological structure [PDF]
This paper addressed the concept of Neutrosophic nano ideal topology which is induced by the two litereture, they are nano topology and ideal topological spaces. We defined its local function, closed set and also defined and give new dimnesion to codense
S. Jafari +5 more
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Chemical Strategies for Multistimuli Responsive Dynamic Covalent Materials in Regenerative Medicine
Multistimuli responsive dynamic covalent materials integrate reversible chemistry with the complex chemical, mechanical, and biochemical cues of regenerative environments. This review highlights chemical strategies based on orthogonal dynamic bonds, multicomponent networks, and hierarchical architectures to regulate mechanics, degradation, and ...
Saurabh Joshi +2 more
wiley +1 more source
The spectrum generated by s-numbers and pre-quasi normed Orlicz-Cesáro mean sequence spaces
In this article, we study some topological properties of the multiplication operator on Orlicz-Cesáro mean sequence spaces equipped with the pre-quasi norm and the pre-quasi operator ideal constructed by this sequence space and s-numbers.
Bakery Awad A.
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Effects of spin symmetry breaking in topological insulators [PDF]
Topological insulators are one of the most thoroughly investigated systems in condensed matter physics over the last years. In these systems, a prominent role is inevitably taken by time-reversal symmetry, which leads to Kramers theorem and symmetry ...
Orth, Christoph
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