Willard Topology Solutions Better _top_ Jun 2026

One infamous exercise (19M in my edition) asks: “Show that a topological space is compact iff every net has a cluster point.” This is a standard result now, but Willard’s presentation is unique: He defines nets just 3 pages earlier, then gives 12 corollaries in the exercises without proof — essentially forcing you to prove Tychonoff’s theorem for nets before he states it.

Thus, the most elegant “solution” to a Willard exercise is not an answer key — it’s the observation that . Problem 17F implies Theorem 18.3. Problem 21B is a counterexample to a plausible conjecture in 22A. In other words, the structure of the exercise set is a solution to the meta-problem: How do you teach a student to think like a topologist? willard topology solutions better

For advanced students and mathematicians, Stephen Willard’s General Topology One infamous exercise (19M in my edition) asks: