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Question: 1 (a) Suppose that X1,......,Xn are topological spaces and Ai, is a subset of Xi, for each i = 1, , n. Prove that int(A1 x......x int(An). Here, int is our notation for taking the interior of a set.
(b) Give an example to show that the equation in part (a) may fail if one considers an infinite product of topological spaces.
Problem 2: Suppose that X and Y are locally compact (but not compact) Hausdorff spaces with one-point compactifications X∞, and Y∞ respectively. Further suppose that (X x Y)∞ denotes the one-point compactification of the locally compact space X x Y.
(a) Let q : X∞ x Y∞ → (X x ')∞ be the map which sends every point of X x Y to itself and sends every other point ∞. Prove that q is a quotient map.
(b) Give an example to how that, in general, X∞ x Yv is not homeomorphic to (X x Y)∞.
Hello I was wondering how fast you could help me with this? Its due soon. There are two attachments. thank you so much!
A widget distributer expects to sell 9000 lots of widgets during the coming year at a steady rate. Yearly carying costs (to be computed on the average number of lots in stock during the year) are $35 per lot
After a year, what will the market share for each firm be? Assume pA = 0.10, pB = 0.15, and pC = 0.20.
An Employee made $388 for the week and sold $103 in product. If the employee gets 20% commission on the products sold and with holding tax is $38 how much is the employees take home pay?
A dog with a leash 5m in length is tied to the outside of a silo with a radius of 20m. What is the approx area the dog has to freely move about?
Compute the centripetal force acting on the body.
settlements in egypt before the time of the pharaohs are dated by measuring the presence of forms of carbon that decay
Find the equation of the least-squares line for the given data. Draw a scatter diagram for the given data and graph the least-squares line.
1) Use the digits of your birthday as the amount of your initial investment (i.e., 6/25 is $625), calculate the value of this investment after 10 years at 3.5% APR for interest compounded yearly, quarterly, monthly, and daily. What do you notice?
a baseball team has home games on thursday and sunday. the two games together earn 3725.50 for the team. thursdays
Thirty students recorded the colors of their eyes, choosing from the colors brown, blue, green, hazel, and black. This data can be appropriately summarized in a
36. A souvenir retailer has an opportunity to establish a new location inside a large airport. The annual returns will depend primarily on the size of the space she rents and if the economy will be favorable. The retailer has worked with the airport ..
Draw a Venn diagram of John's section of the electric company using T = those who cut trees, P = those who climb poles, and W = those who splice wire and label each region with the correct number of employees.
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