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1. Let X be given the co-finite topology. Suppose that X is a infinite set. Is X Hausdorff? Should compact subsets of X be closed? What are compact subsets of X?
2. Let (X,T) be a co-countable topological space. Show that X is connected if it is uncountable. In fact, show that every uncountable subspace of X is connected.
3. Let X be a set and F is separating collection of functions f: X --> Y_f, each from X into a topological space Y_f. Prove that X with the weak topology by F is Hausdorff.
4. Explain how we can think of the unit sphere (a subspace of IR^3 with its usual topology) as a subset of the Hilbert cube.
An observer to a rocket launch was 1800 feet from takeoff position. The observer found the angle of elevation of the rocket as a function of time to be theta=3t/(2t+5).
Let f be defined on the interval [0,1] by setting f(x)=0 if x is irrational, and if x=(m/n) rational where gcd(m,n)=1 set f(x)=n. Show that f is unbounded on every open interval in [0,1] and compute the Lebesgue integral of f over the interval [0,..
Describe an application for the use of ratios or proportions and how it could be useful in your daily life?
State the domain of the following and provide a brief explanation fgor your answer: a) f(x)=sqrtx+4 b) g(x)= 2x+1/x-7 c) h(x)=3x^2+5x-3 d) l(x)=2x+3 e) m(x)=3/x^2+7
A particle is set in motion at time t=0 and moves to the right along the x-axis. (a) Suppose that its acceleration at time t is a=100e^(-1). Show that the particle moves infinitely far to the right along the x-axis.
When the temperture stays the same, the volume of a gas is inversely proportional to the pressure of the gas. If a balloon is filled with 70 cubic inches of gas at a pressure of 14 pounds per square inch
How do I determine the short-run profit maximizing price and quantity? How do I determine the maximum profit accruable to the firm?
Mattel Corporation produces a remote-controlled car that requires three AA batteries. The mean life of these batteries in this product is 35 hours.
Explain Description of Isomorphism, We are working on the proof of showing G (the group of rigid motions of a regular dodecahedron) is isomorphic to the alternating group A_5.
This is the question in my assignment. Give an example of a number you could place in for the variable x, and describe the shift from the original graph. Remember to note what your value you are calculating for the variable x.
Basic probability problems
Find the distance of the ship from the lighthouse.
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