e intersection I In=1 Fn0. Exercise 3.3.6. This exercise is meant to illustrate

Question

e intersection I In=1 Fn0. Exercise 3.3.6. This exercise is meant to illustrate the point made in the opening paragraph to Section 3.3. Verify that the following three statements are true if every blank is filled in with the word "finite." Which are true if every blank is filled in with the word "compact"? Which are true if every blank is filled in with the word "closed"? (a) Every (b) If A and B are (c) If {An : n E N} is a collection of set has a maximum. ,then A + B = {a + b : a E A, b E B} is also sets with the property that every finite subcollection has a nonempty intersection, then As nonempty as well.

Explanation / Answer

a) finite ,compact

closed sets can be unbounded

b) finite, closed,compact

c) finite, compact

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