Mathematics 705

Class Notes and Homework:

• Algebra A set of problems about homomorphisms between C(K) spaces.
• Ascoli A proof of the Ascoli Theorem the Tychonoff product theorem.
• Duals The duals of the classical Banach spaces.
• Tychonoff Some standard applications of the Tychonoff product theorem.
• Vitali A proof of the Vitali covering theorem for measures on metric spaces that satisfy a doubling condition.