Due Wednesday, October 9

* denoted recommended (not graded) problems

A. Let \(X\) be the subset of \(\mathbb{R}^2\): \(X = \{[0,1] \times 0\} \cup \{1/n \times [0,1]: n\in\mathbb{Z}_+\}\cup \{0\times[0,1]\}\). Show that \(X\) is connected and path-connected, but neither locally connected nor locally path-connected.

Section 23 problems 1*, 2*, 3*, 8 and 9
Section 24 problems 1*, 2, 3, and 8*
Section 25 problems 3*, 4*, 7*, and 8