UNIFORMLY APPROACHABLE MAPS 1. Preliminaries Throughout
... let f : X → R. If there exists an uncountable Y ⊆ R such that f −1 (y) is non-empty and connected for every y ∈ Y and that ρ(f −1 (x), f −1 (y)) = 0 for every x, y ∈ Y then f is not W U A. Proof: Replacing X with f −1 (Y ), if necessary, we can assume that X = f −1 (Y ). Now, let D be a countable de ...
... let f : X → R. If there exists an uncountable Y ⊆ R such that f −1 (y) is non-empty and connected for every y ∈ Y and that ρ(f −1 (x), f −1 (y)) = 0 for every x, y ∈ Y then f is not W U A. Proof: Replacing X with f −1 (Y ), if necessary, we can assume that X = f −1 (Y ). Now, let D be a countable de ...
2.3 Some Differentiation Formulas
... 16. Psychology: Learning Rates A language school has found that it’s students can memorize P(t) = 24 t , phrases in t hours of class (for 1 t 10). Find the instantaneous rate of change of this quality after 4 hours of class and interpret your answer. 17. Economics: Marginal Utility Generally, t ...
... 16. Psychology: Learning Rates A language school has found that it’s students can memorize P(t) = 24 t , phrases in t hours of class (for 1 t 10). Find the instantaneous rate of change of this quality after 4 hours of class and interpret your answer. 17. Economics: Marginal Utility Generally, t ...
Day 3
... 3. Odd Multiplicity greater than or equal to 3: The graph crosses the x-axis and it looks like a cubic there. ...
... 3. Odd Multiplicity greater than or equal to 3: The graph crosses the x-axis and it looks like a cubic there. ...
1 Solutions to assignment 3, due May 31
... (b) This is false. Consider A = {0}, and B = C = {a, b}. Let f (0) = a, and let g : B → C be the identity function. Then g ◦ f is not surjective, even though g is. (c) This is false. Consider A = {a, b}, and consider B = C = {0}. If we let f : A → B be given by f (a) = 0, f (b) = 0, and if we let g ...
... (b) This is false. Consider A = {0}, and B = C = {a, b}. Let f (0) = a, and let g : B → C be the identity function. Then g ◦ f is not surjective, even though g is. (c) This is false. Consider A = {a, b}, and consider B = C = {0}. If we let f : A → B be given by f (a) = 0, f (b) = 0, and if we let g ...
