Research Fields
Point-set TopologyPoint-set Topology is the basis of topology, which studies the properties of sets and their relationships. Key concepts include topological space, that is, a set and mathematical objects formed by topological structures defined on the set. Topological structure includes open set, closed set, connectivity and so on. The main research contents of point set topology include continuous mapping, homeomorphism, compactness and separation axiom.
Differential Topology
Differential Topology studies the properties and structure of manifolds, involving differential structures on differential manifolds and the mapping between differential manifolds. Manifold is a kind of space that is locally homeomorphic to Euclidean space. The research objects of differential topology include manifold classification, tangent space on manifold, tangent bundle, smooth mapping and so on. In addition, differential topology also studies the metric, curvature and the relationship between manifolds.
Topological AI
In the field of artificial intelligence, the application of topology has become more and more extensive. The application of topology reveals the unknown interrelationships and inherent laws between data, which provides an important foundation for algorithms such as machine learning and data mining, and not only improves the processing ability of artificial intelligence, but also helps to improve its overall intelligence level.
Mereotopology
In the field of formal ontology (a branch of metaphysics) and in the field of computer and information science ontology, Mereotopology is a first-order theory about the whole, parts, parts of parts and the relationship between parts, which is used to express the concepts of split theory and topology.
Molecular Topology of Organic Chemistry
Molecular Topology of Organic Chemistry is a subject that studies the geometric structure and spatial relationship formed by atoms, chemical bonds and their arrangement in organic molecules. It combines the knowledge of topology and organic chemistry to analyze and predict the relationship between the structure and properties of organic molecules. With the wide application of organic molecules in materials science, energy, optoelectronics and other fields, researchers pay more and more attention to the influence of topological structure on molecular properties.
Topography
Topography mainly focuses on the spatial connection and relationship between topographic features, and does not involve specific geographical locations. It uses topological concepts, such as point, line, surface, boundary and adjacency, to describe the structure and form of terrain. Through the study of topographic topology, we can better understand the complex structure of the earth's surface and the process of topographic evolution.