In mathematics , a metric space is a set together with a metric on the set. The metric is a function that defines a concept of distance between any two members of the set, which are usually called points. The metric satisfies a few simple properties. A metric on a space induces topological properties like open and closed sets , which lead to the study of more abstract topological spaces. The most familiar metric space is 3-dimensional Euclidean space.
Math 440: Topology, Fall 2017
Math , Topology
The class will take an abstract approach, especially around metric spaces and related concepts. For some students, Math will be a suitable alternative to The two classes cover similar material, but will be more fast-paced and have a more abstract and proof-based flavor. If you are in doubt which of the two classes is more appropriate for you, you should come and talk to me as early as possible and certainly before the drop deadline. Math is required for honors majors, and satisfies the WIM requirement.
Homework metric problem solution space
Then is a periodic point with period if and only if. If is negative, then and cannot be -periodic; henceforth assume is nonnegative. Observe and is strictly increasing on.
This class is an introduction to point-set and algebraic topology. Some topics we may cover include topological spaces, connectedness, compactness, metric spaces, normal spaces, the fundamental group, homotopy type, covering spaces, quotients and gluing, and simplicial complexes. Course assistants: Filippos Sytilidis fsytilidis college , Natalia Pacheco-Tallaj pachecotallaj college , and Daniel Qu dqu college , office hours Monday 8pmpm at math night.