# Topology - MATH 254

Undergraduate course, *University of Vermont*, 2022

Introductory course on point set topology.

# Schedule

WEEK 1 - Welcome to M254, sets

WEEK 2 - logic statements, equivalence relation

WEEK 3 - order relation, topological space

WEEK 4 - basis for a topology, theorem always exists a basis

WEEK 5 - finer/coarser, induced topology

WEEK 6 - order topology, interior/closure

WEEK 7 - closure construction theorems

WEEK 8 - limit points, separation

WEEK 9 - continuous func definitions, homeomorphism

WEEK 10 - continuous func construction, metric topology

WEEK 11 - sequence convergence, uniform convergence

WEEK 12 - connected space, intermediate value theorem

WEEK 13 - compactness, compact and Hausdorff

WEEK 14 - extreme value theorem, uniform continuity theorem

WEEK 15 - new definition of compacness, semester review

# Reading material

Munkres - Topology - 2nd Edition

Starbird, Su - Topology Through Inquiry

# Syllabus

Spring 2022 Syllabus

# Lecture notes

Handwritten instructorâ€™s notes

# Grading Notes

The course grade will depend equally on Homework and Final project (40% each). The rest (20%), will be assigned according to the student participation in the course - that includes coming to office hours, or attendance in class, or intervening during lectures - and the work done in class during the in-class quiz.

For the first 3 weeks of class, the homework and in-class quiz will be assigned and I will give feedback on the work done, but irregardless if the proofs are correct or not, the student will be given full mark if they have tried hard enough. My hope is to build up the confidence of students in proving abstract mathematical statements.