## MUNKRES TOPOLOGY HOMEWORK

Concretely, with a small group of students, you will be asked to write a short expository article around pages, typed , and give an in-class 20 min presentation. Here is the exam. Chapter 1 Section 1: Submit final draft to Instructor and Viktor. A more detailed lecture plan updated on an ongoing basis, after each lecture will be posted below. 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.

Continuous functions from subspaces. Covering Spaces Section Examples of connected and non-connected spaces. For more details, see the DSP web site here ; in particular contact information is here. A function between metric spaces is continuous if and only if it is sequentially continuous , meaning the image of a every convergent sequence with limit x is again convergent with limit f x.

## Math 440: Topology, Fall 2017

There will be some emphasis on material covered since the first exam. In complete generality, compactness and sequential compactness both imply limit point compactness, but compactness and sequential compactness are not equivalent and one doesn’t imply the other. Some exercises involving set theoretic identities for instance, De Morgan’s law, applied to the complement of a union or intersection of a family of sets. We will cover other topics as time permits.

yopology Homework 9 is due Friday, November 6. Homework 11 is due Wednesday, November The Hausdorff distance on subsets of a metric space Problem The midterm exam was held on Wednesday, October 4in class e.

The interior of a set. Normal Spaces Section More about subspaces of topological spaces, with examples.

Hutchings’ Introduction to mathematical arguments including a review of logic and common types of proofs. An introduction to metric spaces.

# Math Introduction to Topology I

Students are not allowed to work together on these. Munkres, beginning of 2. The idea that homeomorphisms are “dictionaries” that equate properties involving the topology on one space to properties involving the topology on another space. Homeomorphisms between topological spaces continuous bijections with continuous inversesand an example of a continuous bijection that is not topoloby homeomorphism.

Continuous functions from subspaces.

The Fundamental Group of the Circle Section Submit final draft to Instructor and Viktor. Munkres Topology with Solutions. Hutchinson Dynamical Systems by S. Well-Ordering Chapter 2 Section The Principle of Recursive Definition Section 9: Operations on topological spaces: Review of the Basics Chapter 9 Section A list of some methods for constructing compact subsets: Proofs of some assertions about compact sets: The extreme value theorem.

Closed intervals [a,b] of R are compact in either sense. While the material for the final exam will cover the entire course, there will be somewhat of an emphasis on the material covered after the prelim. As a necessary ingredient, we will recall and develop the language of set theory.

# MTH , Introduction to Topology

This syllabus is not a contract, and the Instructor reserves the right to make some changes during the semester. The instructor strongly adheres to the University otpology regarding principles of academic honesty and academic integrity violations, and will strictly enforce these rules. For now, ignore the definition of “metric topology” or “metrizable” we have not yet defined a “topology” or a “basis for a topology.

More about the interior of a set, and the boundary of a set.