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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
through the point(-2,4) and satifies the given condition L is a vertical line and L2 is the horizontal line and X intercept of L is 3 what is the equation
question the plane passes through the point 151 and is perpendicular to the planes 2x y - 2z 2 and x 3z 4 what is
the student body at eisenhower high school is having an election for homecoming king. the candidates are aaron brad
Two cables are pulling on a steel beam. Both attached at the same location (0, 0). the first cable pulls with a force of 1 500 newtons at a 76° angle and the second cable pulls with a force of 2100 newtons at a 138° angle.
A feasible solution to an LP problem
A gun has a muzzle speed of 50 meters per second. What angle of elevation should be used to hit an object 170 meters away? Neglect air resistance and use g = 9.8 m / sec^{2} as the acceleration of gravity.
A ball is thrown vertically upward with an initial velocity of 96 feet per second. the distance in feet of the ball from the ground after t second is s = 96t - 16t2. For what intervals of time is the ball less than 128 above the ground (after it i..
A garden table and a bench cost $667 combined. The garden table costs $83 less than the bench. What is the cost of the bench?
Filling a tank. A water tank has an inlet pipe and a drain pipe. A full tank can be emptied in 30 minutes if the drain is opened and an empty tank can be filled in 45 minutes with the inlet pipe opened.
Finding the side lengths of the given triangle - Evaluate the vertices of the triangle such that its area is a minimum.
A soft-drink cup is in the shape of a right circular cone with capacity 250 ml. If the radius of the circular base is 5 cm, how deep is the cup?
What is the probability that a freshman selected at random from this group is enrolled in.
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