**Duration:**

**Number of lectures per week:** 3

**Assessment:** Regular assignments

**End-of-year Examination:** One 3-hour examination

**Description: **
The aim of the course is to provide an introduction to metric and
topological spaces in sufficient depth that students will be comfortable
with the use of these concepts in many other branches of mathematics.
The course will begin by introducing concepts of interior and closure, open and closed sets,
convergence and continuity, first in the contexts of subsets of Euclidean spaces,
then in the context of metric spaces, and finally in the context of
topological spaces. Further topological properties such as compactness and
connectedness will be investigated. The course will conclude with
an introduction to algebraic topology, including the concepts of homotopy
and the fundamental group.
If time permits, applications will be given to the topology of the plane, including
Fundamental Theorem of Algebra and the
two-dimensional case of Brouwer's Fixed Point Theorem.

Additional information and feedback form can (or will) be found at

`http://www.maths.tcd.ie/~zaitsev/212.html`

REFERENCES:

In the beginning the course will follow the book

W.A. Sutherland, *Introduction to Metric and Topological spaces*, Oxford University Press (1975)

and partially the book

G. F. Simmons, *Introduction to topology and modern analysis*, McGraw Hill Book Co., (1963)

For other references see the lecture notes by David Wilkins

`http://www.maths.tcd.ie/~dwilkins/Courses/212/`

`http://www.maths.tcd.ie/~dwilkins/Courses/421/`

and the books:

K. Kuratowski, *Introduction to set theory and topology*, Pergamon Press, (1972)

C. W. Patty, *Foundations of topology*, PWS-KENT Publishing Co., Boston, MA, (1993)

W. Rudin, *Principles of mathematical analysis*, McGraw-Hill Book Co., (1976)

J. Dieudonné, *Foundations of modern analysis.*, Academic Press, (1969)

Oct 11, 2004

File translated from T

On 11 Oct 2004, 00:10.