A Bill To Regulate Homework

Solutions to homework problems

1 Homework Assignment # 1 1. Show that the -δ definition of continuity of a map f : X → Y between metric spaces is equivalent to the definition of continuity in terms of open subsets. Proof. Suppose f is -δ-continuous (i.e., continuous in the sense of the -δ definition of continuity) and that U is an open subset of Y . We need to show that f−1(U) is an open subset of X. The definition of an ope...

A Personal Tribute to Bill Lawvere

This year marks the 50th anniversary of Lawvere’s thesis on algebraic theories and of the far-reaching idea of algebraic structure as a functor adjoint to semantics. Around the time of this important event, Lawvere was also thinking about several other questions in category theory, motivated by his manifold interests from logic to physics, passing through algebra. In fact, so much so, that it w...

A bill of rights, or a bill of goods?

In response to the rise in construction defect litigation and the resulting increase in the cost of insurance contractors are required to carry, the Washington Legislature passed RCW 64.50.005 et seq., which became effective June 13, 2002. The statute (referred to by some as a “bill of rights” for contractors) requires that homeowners and condominium homeowners’ associations (collectively “home...

Sample Solutions to Homework # 4

Introduction to Proofs: Homework Solutions