This cluster addresses topological concepts, such as the lifting of curves on a torus to the Euclidean plane, and properties of Tychonoff spaces with respect to their Stone-Čech compactifications. It also deals with the question of isolating points in almost discrete spaces. The research involves proving geometric theorems and understanding the structure of various types of topological spaces, particularly with regards to convergence and embeddings.
This cluster revolves around advanced mathematical topics. It includes a question on the proof of Cayley’s Theorem for Topological Groups and another related to the analytic continuation of a complex function involving the sinc function and the polylogarithm function, and includes the digamma function too. The use of topological groups and integral representations of functions makes these problems relevant to the field of mathematical analysis and abstract algebra.
This cluster covers topics in geometry and topology. It explores trajectory behavior in planar polynomial ODEs, examines a paradox involving probability of acute triangles in different geometries and also provides a geometrical interpretation for the sum of the first n cubes. It touches on how quaternions can be used to derive the equations of spherical trigonometry.