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1. Show that the closure of a nowhere dense set is nowhere dense.
2. Let (S, d) and (V, e) be two metric spaces. On the Cartesian product S × V take the metric ρ((x, u), (y, v)) = d(x, y) + e(u, v).
Show that the completion of S × V is isometric to the product of the completions of S and of V .
3. Show that the intersection of the complement of a set of first category with a non-empty open set in a complete metric space is not only non-empty but uncountable. Hint: Are singleton sets {x } nowhere dense?
How would you use the "margin of error" in estimating the percentage of all adults who think that Venetian blinds are the hardest to clean?
The Minneapolis Tribune ran an article on gender differences in shopping behavior. When 400 women were asked to respond to the question "Where I shop is influenced by which store has a greater variety," 60% answered "Yes.
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computing probability values using normal distribution.in a population of test scores not known to be normally
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