Topology
4 points * First semester * Clayton * Prerequisites: MAP2011 and one other second-year MAP subject
Objectives On the completion of this subject students will be able to understand the basic concepts of topology; open and closed sets, closure, interior and boundary of a set with special emphasis on metric spaces; understand the notions of continuity, especially homeomorphism, and recognise them in particular examples from calculus and analysis; manipulate the above concepts in simple situations, especially in examples from other branches of mathematics, notably calculus and analysis; understand the concepts and basic properties of connected and compact spaces especially in examples from analysis; reproduce proofs of theorems concerning topological and metric spaces in some straightforward cases.
Synopsis Topological spaces, continuous maps and homeomorphisms. Subspaces and products. Bases for open sets. Connectedness and compactness.
Assessment Examinations (1.5 hours): 70% * Assignments: 30%
Recommended texts
Baker C W Introduction to topology W C Brown, 1991
Giles J R Introduction to the analysis of meetric spaces AMS Lecture Series 3
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