International Mathematics Master 2026-27
Lahore - Pakistan
Fall 2026
ADVANCED TOPOLOGY
Hanyia Azam and Laura Geatti
Program: This course has been designed as an introduction to general topology. This course covers basic
point set topology and will be followed by introductory Algebraic topology. We will revisit metric spaces and
study basic notions for topological spaces. We will learn topological properties connectedness and compactness.
Constructions such as product spaces and quotient spaces will also be discussed.
Algebraic topology associates algebraic structures with a topological space. The first algebraic invariant is that of
the fundamental group. We will cover the fundamental group and their connection with covering spaces. Finally,
we will introduce Homology theory, compute examples and learn applications.This course covers basic
point set topology and introductory algebraic topology.
Basic notions for topological spaces; connectedness, compactness;
product spaces, quotient spaces; metric spaces.
Algebraic topology associates algebraic structures with a topological space. The first algebraic invariant is that of
the fundamental group. We will cover the fundamental group and their connection with covering spaces.
Prerequisites: a background in Set Theory (and preferably some knowledge of Real Analysis - I).
Texts:
- J. R. Munkres, Topology, Pearson 2013.
- A. Hatcher, Algebraic Topology, pdf
Exercises:
Lectures overview: