Albion College

Mathematics and Computer Science

Mathematics and Computer Science

COLLOQUIUM

The Naked Truth About The Baire Category Theorem

Clifford Weil

Professor

Department of Mathematics

Michigan State University

Professor

Department of Mathematics

Michigan State University

The talk will begin with a narrow discussion of the notion of a metric space. Examples presented will be those used later. Then the Baire Category Theorem will be stated and discussed. Finally the theorem wil be applied to prove the existence of a certain difficult to construct examples such as an everywhere continuous, but no where differentiable function. All will be connected to familiar concepts from calculus and will require theorems from advanced calculus.