Special Topics in Topology
20 credits / 30 lectures and a weekly one hour tutorial
The course intends to cover several topics from analytic topology that have connections to many related mathematical fields like functional analysis, algebraic topology, lattice theory and category theory. We shall mainly concentrate on fundamental ideas about uniform topological structures that lead to numerous and sometimes obvious applications in many fields of analysis, topological algebra and order theory. Detailed literature will be announced during the course. There is no prescribed text. Recommended books for further reading:
- I.M. James, Introduction to Uniform Spaces, Cambridge, 1990.
- R. Engelking, General Topology, Heldermann, 1989.
Contents to be covered:
- Uniform spaces and their completions.
- Proximities and compactifications; connections to totally bounded uniformities.
- Topological groups (left, right and two-sided uniformities).
- Topologies and uniformities on function spaces resp. hyperspaces.
- Connections between topology and order.
Examining: marked homework (totalling 40% of final mark) plus one written examination of 2 hours in October/November 2018 (totalling 60% of final mark).
Prerequisites:The Honours Topology Core module is highly recommended.