221 Analysis (First Semester) 200809
Lecturer: Derek Kitson
Course Outline:

This course will begin with an introduction to metric spaces including
open and closed sets, convergence, equivalence of metrics,
continuity and completeness.
Following this we will look at topological spaces, the separation axioms, compactness and connectedness.
Course summary: (23rd January)

A summary of the course can be found
here.
This includes all definitions and the statements of all lemmas, propositions and theorems. Some examples are also included.
Note: Information on nonexaminable material for this semester can be found here.
Assignments:
 Assignment 1 ha1.pdf Date due: Friday 7th November
 Assignment 2 ha2.pdf Date due: Friday 28th November
 Assignment 3 ha3.pdf Date due: Friday 9th January
 Assignment 4 ha4.pdf Date due: Friday 23rd January
 Selected solutions (updated January 28th) soln.pdf
Recommended Reading:
 Lecture notes to previous years 221 course by David Wilkins are here.
 Paschalis Karageorgis has collected a number of problems relating to metric spaces and topology and their solutions here.
 Introduction to Metric and Topological Spaces, W.A. Sutherland (Oxford University Press, 1975)
 Introduction to Analysis of Metric Spaces, J.R. Giles (Cambridge University Press, 1987)
 Metric Spaces, M. O'Searcoid (Springer Undergraduate Mathematics Series, 2007)
 Topology: a first course, J.R. Munkres (PrenticeHall, Inc., 1975)
 General Topology, S. Willard (AddisonWesley Publishing Company, Inc., 1970)
 General Topology, J.L. Kelley (D. Van Nostrand Company, Inc., 1955)
Questions and comments to dk@maths.tcd.ie
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