Hutchinson Dynamical Systems by S. We will cover other topics as time permits. Time permitting, we may include other topics, such as the fundamental group of a topological space. Students are not allowed to work together on these. You may work with others and consult references including the course textbook , but the homework you turn in must be written by you independently, in your own language, and you must cite your sources and collaborators. The final exam will be cumulative, but will have greater emphasis on topics developed after the midterm. Topology , 2ed, by James R.
Within this text, we will focus on Part I, particularly Chapters and other portions on an as-needed basis. At least one problem will be taken from a previous homework assignment At least one problem will be a minor variation of a problem on the midterm exam The length and difficulty of the final exam problems will be similar to those of the homework and the midterm exam. The Metric Topology Section If Y is a subset of X, then the two notions of compactness we’ve discussed for Y as a subset of X, and for Y thought of as asubspace agree. Any student requesting academic accommodations based on a disability is required to register with Disability Services and Programs DSP each semester.
At least two of the problems on the final will be “very familiar”, in the following sense: Welcome and overview of class e. We will cover other topics as time permits.
The extreme value theorem. Homework 9 half weight.
Continuous Functions Section A list of some methods for constructing compact homdwork The Principle of Recursive Definition Section 9: The project assignment is posted here. We will also apply these concepts to surfaces such as the torus, the Klein bottle, and the Moebius band. A more detailed lecture plan updated on an ongoing basis, after each lecture will be posted below.
MTH , Introduction to Topology
Every function from a discrete metric space is continuous. You are free to devise whatever strategy for learning the material suits you best.
Thursdays pm, in Malott This course covers basic point set topology, in particular, connectedness, compactness, and metric spaces. The exam will have a total of six problems, of which students will be required to complete any four.
The grading will be based on the homework and the take-home examinations. Examples of non-metrizable topological spaces. Topo,ogy idea that homeomorphisms are “dictionaries” that equate properties involving the topology on one space to properties involving the topology on another space.
Compact Spaces Section You can handwrite your solutions, but you are encouraged to consider typing your solutions with LaTeX. More examples around connectedness: Students may work together on homework but must write up their work individually.
Subspaces of topological spaces.
Online resources Notes on the Tychonoff theorem by Pete L. Topoloogy will be some emphasis on material covered since the first exam. Behavior of open sets with respect to union and intersection.
Math 440: Topology, Fall 2017
An introduction to metric spaces. Chapter 1 Section 1: Limit Point Compactness Section Components and Local Connectedness Section Covering Spaces Section Direct Sums of Abelian Groups.
A function between metric spaces is continuous if and only if it is sequentially continuousmeaning the image of a every convergent sequence with limit x mnkres again convergent with limit f x. A subset of R equipped with the subspace topology is connected if and only if it is an interval.
If X is compact, then X is limit point compact.