Question

In: Advanced Math

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.

Solutions

Expert Solution


Related Solutions

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]
Find the derivative of the function. A) f(x)=(2+x^3)^2/3 B) h(t)= (t^4-1)^9(t^3+1)^8 C) y = e4x sin(x)...
Find the derivative of the function. A) f(x)=(2+x^3)^2/3 B) h(t)= (t^4-1)^9(t^3+1)^8 C) y = e4x sin(x) D) y= (x^2+2/x^2-2)^3
1.Find the equation of the tangent to x=t^2-t, y=t^2+t+1, at the point t=1 2.Find the length...
1.Find the equation of the tangent to x=t^2-t, y=t^2+t+1, at the point t=1 2.Find the length of the curve x=t*sint, y=t*cost, 0≤t≤1
given the curve x(t)=t^2+3 and y(t)=2t^3-3t^2 find the following: a.) find the derivative of the curve...
given the curve x(t)=t^2+3 and y(t)=2t^3-3t^2 find the following: a.) find the derivative of the curve at t=1 b.) dind the concavity of the curve c.) graph the curve from t=0 to t=2 d.) find the area if the curve on the interval 0<=t<=2
Let f(x)=(x^2+1)*(2x-3) Find the equation of the line tangent to the graph of f(x) at x=3....
Let f(x)=(x^2+1)*(2x-3) Find the equation of the line tangent to the graph of f(x) at x=3. Find the value(s) of x where the tangent line is horizontal.
Let f(x,y)= (3/2)(x^2+y^2 ) in 0≤x≤1, 0≤y≤1. (a) Find V(X) (b) Find V(Y)
Let f(x,y)= (3/2)(x^2+y^2 ) in 0≤x≤1, 0≤y≤1. (a) Find V(X) (b) Find V(Y)
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT