A list of some methods for constructing compact subsets: Examples of non-metrizable topological spaces. Make-up quizzes will NOT be given. Reading After finishing our discussion of the Arzela-Ascoli-Frechet theorem and the compact-open topology, we will cover as many of the following topics as the remaining class time allows: Nets Chapter 4 Section
Homework 9 half weight. The main result we covered is discussed in Munkres 2. Examples of non-metrizable topological spaces. For more details, see the DSP web site here ; in particular contact information is here. Cartesian products and functions between sets. The Principle of Recursive Definition Section 9:
Submit first draft to Instructor and Viktor.
A portion of your class grade will be based upon a munkers exploring an aspect of topology beyond the topics covered in class. The Urysohn Lemma Section Thursdays pm, in Malott This course covers basic point set topology, in particular, connectedness, compactness, and metric spaces.
Munkres (2000) Topology with Solutions
If required, please make sure that the DSP muunkres for approved accomodations is delivered to me as early in the semester as possible. A list of some methods for constructing compact subsets: Cartesian products and functions between sets. Homework 6 is due Wednesday, October 7.
More about continuity being equivalent to sequential continuity. Continuous Functions Section The instructor strongly adheres to the University policies regarding principles of academic honesty and academic integrity violations, and will strictly enforce these rules.
Math 440: Topology, Fall 2017
Hway Kiong Lim E-mail: 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.
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.
The extreme value theorem. More about the quotient topology: Homework 10 is due Monday, November More about the interior of a set, and the boundary of a set.
Math Introduction to Topology I
Our primary goal this semester will be to get through the first four chapters of Munkres’ book. The Countability Axioms Section A review of logic particularly statements such as “If Mun,res then Q” and variants such as the contrapositive, converse, and negation.
Continuous functions from subspaces.
The grading will be based on the homework and the take-home examinations. Unions of subsets which are each connected in the subspace topology and which have non-empty intersection remain connected.
Remember, you are doing the homework in order to learn the material; don’t try to defeat the purpose of it.
Finite products of connected spaces are connected.
Topology provides the language of modern analysis and geometry. A more detailed lecture plan updated on an ongoing basis, after each lecture will be posted below. The Integers and the Real Numbers Section 5: The definition of an abstract topological space. Chapter 1 Section 1: More about subspaces of topological spaces, with examples. Sequences and convergent sequences in a metric space.
Homework 4 is due Monday, September About the final exam The final exam will be held on Monday, December 7, 1: