Chapter 12.1, Problem 4E

Interpretation Introduction

Interpretation:

Let $\text{B}$ be the baker’s map with $\text{a <}\frac{1}{2}$. The figure shows that the set ${\text{B}}^{\text{2}}\left(\text{S}\right)$ consists of horizontal strips separated by vertical gaps of different sizes.

Find the size of the largest and smallest gaps in the set ${\text{B}}^{\text{2}}\left(\text{S}\right)$.

Redo part $\left(\text{a}\right)$ for ${\text{B}}^3\left(\text{S}\right)$.

Finally, answer the question in general ${\text{B}}^{\text{n}}\left(\text{S}\right)$.

Concept Introduction:

Consider $\text{B}$ as the baker’s map with $\text{a < }\frac{\text{1}}{\text{2}}$. Refer the figure that shows the set ${\text{B}}^{\text{2}}\left(\text{S}\right)$ consisting of horizontal strips separated by vertical gaps of different sizes.