Topology

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

1. Warm-up

   In $\mathbb{R}$ with the standard topology, let $S = [0, 3] \cup \{1, 2, \ldots, 6\}$. How many connected components does $S$ have?

2. Warm-up

   In $\mathbb{R}$ with the standard topology, let $S = [0, 4] \cup \{1, 2, \ldots, 9\}$. How many connected components does $S$ have?

3. Warm-up

   In $\mathbb{R}$ with the standard topology, let $S = [0, 2] \cup \{1, 2, \ldots, 4\}$. How many connected components does $S$ have?

Problems shown under their original terms: Generated (template, solver-computed).