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If f: X->Y is transversal to Z and dim X + dim Z = dim Y, then we can at least define I_2(f, Z) as #f^(-1)(Z) mod 2, as long as f^(-1)(Z) is finite. Let us explore how useful this definition is without the two assumptions made in the text: X compact and Z closed. Find Examples to show:(a) I_2(f, Z) may not be a homotopy invariant if Z is not closed.(b) I_2(f, Z) may not be a homotopy invariant if X is not compact.(c) The Boundary Theorem is false without the requirement that Z be closed.(d) The Boundary Theorem is false without the requirement that X be compact.(e) The Boundary Theorem is false without the requirement that W be compact, even if X = dW is compact and Z is closed. (Hint: Look at the cylinder S^1 * R.)Reference: Ex 2.4.13 of Guillemin
A poster is to have an area of 160 in2 with 1 inch margins at the bottom and sides and a 3 inch margin at the top. What dimensions will give the largest printed area?
The price of a gallon of unleaded gas has risen to $2.88 today. Yesterday's price was $2.81 . Find the percentage increase. Round your answer to the nearest tenth of a percent.
Should You Believe a Statistical Study - Is there bias in the sample used in the study and are there any problems in defining or measuring the variables of interest in the study?
two cars leave a city and head the same direction. after 6 hours, the faster car is 48 miles ahead of the slower car. the slower car has traveled 252 miled. find the speeds of the two cars.
Decision Analysis with Decision Tree, Jack Nimble, an employee of Daniel Construction Company, claims to have injured his back as a result of a fall while repairing the roof at one of the Eastview apartment buildings
points a & b are the midpoints of adjacent sides of the square. what is the value of the shaded part?
Find the differential coefficient for three different functions to demonstrate the use of function of a function and the product and quotient rules and use integral calculus to solve two simple engineering problems involving the definite and indefi..
Identify the statistical measures that would be used to analyze the data and calculate those measures, and explain your choice.
Assume that the average annual salary for a worker in the United States is $28,500 and that the annual salaries for Americans are normally distributed with a standard deviation equal to $6,250. Find the following
Prestige Builders has a development of new homes. There are four different floor plans, seven exterior colors, and an option of either a two-car or a three-car garage. How many choices are there for one home?
A chain store manager has been told by the main office that daily profit, P, is related to the number of clerks working that day, x, according to the function P=-25x^2+300x. What number of clerks will maximize the profit, and what is the maximum p..
Compute the time and cost
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