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1. Prove that, in a topological space X, if U is open and C is closed, then U - C is open and C - U is closed.
2. Which sets are closed sets in the finite complement topology on a topological space X?
3. Let X be a topological space.
(a) Prove that Φ and X are closed sets.
(b) Prove that the intersection of any collection of closed sets in X is a closed set.
(c) Prove that the union of finitely many closed sets in X is a closed set.
4. Show that R in the lower limit topology is Hausdorff.
5. Show that R in the finite complement topology is not Hausdorff.
6. Which sets are closed sets in the particular point topology PPX p on a set X?
Find the velocity, speed and acceleration of the vector-valued function: Vector r = cost i + sint j - 16t^2 k at t=pi/4
Each unit produced costs the company $8.00, and is sold for $10.00. How much will the company gain or lose in a month if they stock the expected number of units demanded, but sell 2000 units?
What is the rate of change of the radius of the lower ball at moment when the radius of the middle ball is 12in?
A car is traveling at 90 km/h when the driver sees an accident 50 m ahead and slams on the brakes. What constant deceleration is required to stop the car in time to avoid a pileup? (Give your answer correct to two decimal places.)
Calculate the ratio of the area to the volume for a unit cube, a unit sphere inscribed inside the cube, and a right cylinder inscribed inside the cube.
How much should the bank invest in each possible category? Let x, y, and z, respectively, be the amounts invested in bonds, certificates of deposit, and first mortgages. Solve the system of equations by the Gauss-Jordan elimination method.
a class budget consist of $900 for dances, $1,200 for trips, and $600 for charity. If the data were presented in a circle graph, what would be the angle measure of the part labeled "dances"?
Sketch the Graph of y = cosx in the range -Pi
A computer processes jobs on a first-come first-serve basis in a time-sharing environment. The jobs have Poisson arrival rates with an average of six minutes between arrivals.
Which of the following is/are characteristic(s) of a binomial probability experiment?
A person repeatedly and independently flips a coin to decide whether to take a step to the left or to the right from a point X. determine the expected number of times the person returns to X.
In spring 2006 the average monthly rent was $1,355, an increase of 3.6percent from 2005. What was the average monthly rent in 2005.
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