1. Introduction ................................................. 5
2. Background and notation ...................................... 7
3. Examples of Banach spaces ................................... 11
4. Semigroups and weights ...................................... 13
5. Sets determining for the topological centre ................. 23
6. Examples of weights ......................................... 30
7. Algebras on subsets of I .................................... 34
8. Continuous weights on R+ .................................... 37
9. Conditions for Arens regularity ............................. 39
10.A weight on N ............................................... 46
11.A strange weight on Q+ ...................................... 49
12.Open questions .............................................. 56
13.Summary ..................................................... 56
References ..................................................... 57
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