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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?
What is the area of the shaded region? Assume the hexagon is regular. The length is 22 the apothem is 19.05.
find the slope of an object either where you live, where you work, or outside somewhere. Examples might include a ladder positioned against a wall or against a house, a banister on a set of stairs, a slide in a park, etc.
A company uniformly receives 20 phone calls from 9am -7 pm What is the probability that the number of calls between 12 :00 and 1:00 will be:
maddie owns a hog farm.she sends hogs to market in a ratio of 3 to 10 on mondays and tuedays.if maddie sent 333 hogs to the market on monday, how many did she send to market on tuesdays.
Test at the five percent level of significance
a pizza company claims that it puts 0.5 kg of cheese in its pizza of a certain size. the amount of cheese on a randomly selected pizza of this size is normally distributed with a mean of 0.5 kg and standard deviation of 0.025 kg.
Orbit of Venus. If the average radiu of the orbit of Venus is 0.723AU, then how many years does it take for Venus to complete one orbit
Suppose that S and T are sets of size m and n, respectively. Choose a representation of these sets that makes it possible to implement Intersection(S,T), which returns S ? T , in time O((m + n) log m). Explain how the intersection is found and arg..
Seawater has density 1025 kg/m3 and flows in a velocity field v=yi+xj, where x ... where x, y, and z are measured in meters and the components of v in meters per second. Find the rate of the flow outward through the hemisphere x2+y2+z2=9, z >0
Find the derivative of the function.
Suppose that f_n(0) converges to some number, denoted f(0), and also suppose that the sequence (f'_n) converges uniformly on (0,1) to some function g: (0,1) -> R. Prove that the sequence (f_n) converges uniformly. What is its limit?
The Action Sports Network surveyed 265 of its viewers to determine which sports they watched most often. The results of the survey showed:
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