This course introduces topology, covering topics fundamental to modern analysis and geometry. It also deals with subjects like topological spaces and continuous functions, connectedness, compactness, separation axioms, and selected further topics such as function spaces, metrization theorems, embedding theorems and the fundamental group.

Topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing ...

2020年5月23日 · There is a full video course in Youtube: General Topology - ICTP. It covers chapters 2,3,4 and 9 (topological spaces and continuous functions, connectedness and compactness, countability and separation axioms, the fundamental group) of a standard textbook: Munkres - Topology.

Learn Topology or improve your skills online today. Choose from a wide range of Topology courses offered from top universities and industry leaders. Our Topology courses are perfect for individuals or for corporate Topology training to upskill your workforce.

To present an introduction to the field of topology, with emphasis on those aspects of the subject that are basic to higher mathematics. To introduce the student to what it means to do mathematics, as opposed to learning about mathematics or to learning to …

Topology is simply geometry rendered exible. In geometry and analysis, we have the notion of a metric space, with distances speci ed between points. But if we wish, for example, to classify surfaces or knots, we want to think of the objects as rubbery. Examples. For a topologist, all triangles are the same, and they are all the same as a circle.

Topics include: Singular homology, CW complexes, Homological algebra, Cohomology, and Poincare duality. Freely sharing knowledge with learners and educators around the world. Learn more. This is a course on the singular homology of topological spaces.

2025年1月6日 · A course in general topology. Topological spaces: metric spaces, subspaces, continuous maps, connectedness, separation axioms; topological vector spaces: Hilbert spaces, Banach space, Frechet spaces; the quotient topology or identification spaces: the classification of two-dimensional manifolds; fundamental group and covering spaces; covering ...

Point set topology, topological spaces and metric spaces, continuity and compactness, homotopy and covering spaces

MTH 4030 – Topology. This class introduces the fundamental and unifying concepts of one of the pillars of contemporary mathematics – point-set, or general, topology. Topics covered are metric spaces, general topological spaces, connectedness, and compactness.