School of Mathematics
MA3421:
Functional Analysis I
Tutorial and exercise sheets
- Tutorial Sheet 1 [October 6]
- Metric topologies - some examples.
- Tutorial Sheet 2 [October 13]
- Bases for toplogies. Product topology on $\mathbb R^2$.
- Tutorial Sheet 3 [October 20]
- Equivalent metrics example. Countable products of metric spaces.
- Tutorial Sheet 4 [October 20]
- Weak topologies. First countable spaces.
- Tutorial Sheet 5 [October 27]
- Absolutely convergent series in Banach spaces.
- Tutorial Sheet 6 [November 17]
- An example of an isometric isomprphism (between the space of convergent sequences and continuous
functions on a compact subset of the real line).
- Tutorial Sheet 7 [November 24]
- $\ell^p$ is separable. Hölder's inequuality.
- Tutorial Sheet 8 [December 1]
- Boundedness of some multiplication operators (as examples of bounded linear operators).
- Tutorial Sheet 9 [December 8]
- Baire catgeory, Open mapping theorem.
