Topology Syllabus & Review Problems for the Comprehensive
January 1, 2010
Topics Covered: The Core-I comprehensive examination in topology will cover the
fundamentals of two topics: General Topology of Point Sets and Homotopy Theory and
LECTURE 7: EXCISION PROPERTY AND MAYER-VIETORIS SEQUENCE
In this lecture we will state the important excision property of singular homology while the
proof of this important property will only be given in the next lecture. Here we want to draw some
This note is meant to give a short introduction to CW complexes.
1. Notation and conventions
In the following a space is a topological space and a map f : X Y between topological spaces
X and Y is a function which is continuous.
Topology and Geometry Prelim, June 2012
Show your work and justify your answers. The score for this exam will be based on the three
best answers from each section. Two perfect answers from each section are sucient for a
best possible score of 1 on the pre