MATE 6540   Topology

Time and place

MJ 15:00--16:15, in N-204.

Topics The course will consist of two parts:

First (and core) part: point-set topology: review of topological space, limits and continuity, construction of topological spaces, compactness, limits of functions, numerical functions, connectedness.

Second part: depending on students' interest, the second part may consist of:
(a) Algebraic topology: homotopic paths, fundamental group, induced homomorphism, covering space, index and applications, homotopic maps, or
(b) Differential topology: smooth manifolds and smooth maps, the theorem of Sard and Brown, the degree modulo 2 of a mapping, or:
(c) Applications of topology to analysis: summable families and infinite sums, elementary theory of normed spaces, geometry of Hilbert space.

References

"General topology", by Jacques Dixmier, Springer-Verlag, 1984.

"Introduction to Topology", by T.W. Gamelin & R.E. Greene, Dover, 1999.

"Topology from the differentiable viewpoint", by John Milnor, University Press of Virginia, 1965, 1969 - if we chose to include this topic.

Evaluation

Based on homework, exams.

Homework you may collect the last homework sets from my office, Monday May 16, 17:00--19:00.

Last modified: Mon May 16 15:13:20 AST 2016