Let X = {1, 2, 3}. Find all topologies T on X such that (X, T...

Let X = {1, 2, 3}. Find all topologies T on X such that (X, T ) is regular.

Expert Solution

Colby Messinger answered 1 year ago

3. Let X = {1, 2, 3, 4}. Let F be the set of all functions...

3. Let X = {1, 2, 3, 4}. Let F be the set of all functions from X to X. For any relation R on X, define a relation S on F by: for all f, g ∈ F, f S g if and only if there exists x ∈ X so that f(x)Rg(x). For each of the following statements, prove or disprove the statement. (a) For all relations R on X, if R is reflexive then S is reflexive....

Let X = [1, 0, 2, 0]tand Y = [1, −1, 0, 2]t. (a) Find a...

Let X = [1, 0, 2, 0]tand Y = [1, −1, 0, 2]t. (a) Find a system of two equations in four unknowns whose solution set is spanned by X and Y. (b) Find a system of three equations in four unknowns whose solution set is spanned by X and Y. (c) Find a system of four equations in four unknowns that has the set of vectors of the form Z + aX + bY as its general solution where...

Let ¯r(t) = < t, t^2 , t^3 >be a twisted cubic. a) Find the osculating...

Let ¯r(t) = < t, t^2 , t^3 >be a twisted cubic. a) Find the osculating circle for this twisted cubic at t = 0. b) Try to do the same for the ordinary cubic parabola ¯r(t) = <t, 0, t^3 >. Explain why did you fail to do that.

4. Let r(?) = �?, 4 3 ? 3/2, ?2 �. (a) Find T, N, and...

4. Let r(?) = �?, 4 3 ? 3/2, ?2 �. (a) Find T, N, and B at the point corresponding to ? = 1. (b) Find the equation of the osculating plane at the point corresponding to ? = 1. (c) Find the equation of the normal plane at the point corresponding to ? = 1

Let f(x) = x^4 - 4x^3 - 18 x^2 + 77 a) a) Find all critical values of the...

Let f(x) = x^4 - 4x^3 - 18 x^2 + 77 a) a) Find all critical values of the function. [10] b) b) Find all intervals of increase and decrease. [10] c) Find all relative extrema. Use the second derivative test. Label each as a relative max. or a relative min. [10] d) d) Find on what interval(s) the function is concave up and concave down. [10] e) e) Find all inflection point(s), if any, of the function. [10]

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Let X = {1, 2, 3}. Find all topologies T on X such that (X, T...

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3. Let X = {1, 2, 3, 4}. Let F be the set of all functions...

Let X = [1, 0, 2, 0]tand Y = [1, −1, 0, 2]t. (a) Find a...

Let ¯r(t) = < t, t^2 , t^3 >be a twisted cubic. a) Find the osculating...

4. Let r(?) = �?, 4 3 ? 3/2, ?2 �. (a) Find T, N, and...

Let f(x) = x^4 - 4x^3 - 18 x^2 + 77 a) a) Find all critical values of the...

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