Topology is a branch of mathematics concerned with the properties of space that are preserved under continuous deformations, such as stretching and bending, but not tearing or gluing. It emerged from geometry and set theory, through the analysis of concepts like continuity, compactness, and connectedness. The key idea in topology is the concept of a topological space, which generalizes the notion of geometric shapes in a more abstract form. Topology can be divided into several subfields such as point-set topology, which deals with the more foundational set-theoretic definitions and properties; algebraic topology, which studies spaces with tools from abstract algebra; and differential topology, which focuses on differentiable functions and their implications. This field has wide applications across various areas of mathematics and science, including the study of dynamical systems, computational biology, and physics, particularly in understanding the properties of space and time and the behavior of the universe at a large scale.

Researchers state that finely crafted interfaces provide innovative design approaches that go beyond traditional materials, with potential applications in infrared optics, sensing, and other areas….

New studies show photon polarization is constant in varying environments, potentially improving plasma heating methods for fusion energy advancement. Light, both literally and figuratively, pervades…

A KAIST-led research team has successfully demonstrated the internal three-dimensional polarization distribution in ferroelectric nanoparticles, paving the way for advanced memory devices capable of storing…

Researchers from an international consortium have published a groundbreaking study that advances the field of solid-state physics. An international group of researchers has found that…

Researchers at AMOLF, working alongside colleagues from Germany, Switzerland, and Austria, have realized a new type of metamaterial through which sound waves flow in an…

Researchers from the High Magnetic Field Center of the Hefei Institutes of Physical Science of the Chinese Academy of Sciences and the University of Science…

Generally, it’s advised not to compare apples to oranges. However, in the field of topology, a branch of mathematics, this comparison is necessary. Apples and…

Researchers at the University of Würzburg have developed a method that can improve the performance of quantum resistance standards. It’s based on a quantum phenomenon…

Innovative research introduces a practical, model-free method for exploring topological properties in materials, enhancing the scope and efficiency of topological studies. The branch of mathematics…

In 1960, Luttinger proposed a universal principle connecting the total capacity of a system for particles with its response to low-energy excitations. Although easily confirmed…

Dozens of research papers have characterized a substance composed of europium, cadmium, and arsenic as a Weyl semi-metal, a unique category of exotic topological materials….

In a new study published in The Journal of Finance and Data Science, a researcher from the International School of Business at HAN University of Applied Sciences in…

Materials can host D-wave effects with F-wave behaviors. Physicists from Rice University have demonstrated that immutable topological states, which are highly sought for quantum computing,…

The findings could revolutionize electronics and quantum computing. A breakthrough in a topological insulator material, which possesses insulating properties internally but conductive properties on the…

An international team of researchers has discovered that a novel form of heterostructure made up of layered two-dimensional (2D) materials could help overcome the major…

Topological phases are not limited to electronic systems and can also exist in magnetic materials characterized by magnetic waves, known as magnons. While scientists have…

Searchable tool reveals more than 90,000 known materials with electronic properties that remain unperturbed in the face of disruption. What will it take for our…