![2. [2+9+6=17] Let X be a nonempty set. Two metrics d and d on X are said to be uniformly equivalent if the identity map from](http://img.homeworklib.com/questions/c1b39d10-bbd4-11ea-aaf3-732ebf590e69.png?x-oss-process=image/resize,w_560)
Homework Answers
Add Answer to:
2. [2+9+6=17] Let X be a nonempty set. Two metrics d and d on X are...
Topology 3. Either prove or disprove each of the following statements: (a) If d and p...
Topology
3. Either prove or disprove each of the following statements: (a) If d and p map (X, d) X, then the identity topologically equivalent metrics (X, p) and its inverse are both continuous are two on (b) Any totally bounded metric space is compact. (c) The open interval (-r/2, n/2) is homeomorphic to R (d) If X and Y are homeomorphic metric spaces, then X is complete if and only if Y is complete (e) Let X and Y...
10. Let T1 and T2 be two topologies on a set X. Then T1 is said...
10. Let T1 and T2 be two topologies on a set X. Then T1 is said to be a finer topology than T2 (and T2 is said to be a coarser topology than T1) if Ti2 T2. Prove that (i) the Euclidean topology R is finer than the finite-closed topology on R; (ii) the identity function f: (X, Ti) -(X, T2) is continuous if and only if TI is a finer topology than T2.
Have to get an idea of how i am doing on this problem. Whould be nice...
Have to get an idea of how i am doing on this problem. Whould be
nice to get a good explaination for each part of the problem. d1
and d2 is the two different metrics, p ,Y.
Problem 2. Consider first the following definition: Definition. Let X be a set and let pand be two metrics on X. We say that p and are equivalent if the open balls in (X, p) and (x,y) are "nested". More precisely, p and...
1. (a) Let d be a metric on a non-empty set X. Prove that each of...
1. (a) Let d be a metric on a non-empty set X. Prove that each of the following are metrics on X: a a + i. d(1)(, y) = kd(x, y), where k >0; [3] ii. dr,y) d(2) (1, y) = [10] 1+ d(,y) The proof of the triangle inequality for d(2) boils down to showing b + > 1fc 1+a 1+b 1+c for all a, b, c > 0 with a +b > c. Proceed as follows to prove...
Problem 5. For u = (Uk)x=1,2,... El, we set Tnu = (U1, U2, ..., Un, 0,...)....
Problem 5. For u = (Uk)x=1,2,... El, we set Tnu = (U1, U2, ..., Un, 0,...). (1) Prove that Tn E B(C2, (). (2) We define the operator I as Iu = u (u € 14). Then, prove that for any u ele, lim ||T,u - Tulee = 0. (3) Prove that I, does not converge to I with respect to the norm of B(C²,1). Let X, Y be Banach spaces. Definition (review) We denote by B(X, Y) a set...
(d) Let (x1,x) R..9x 2 yo} (3) S is the set of combinations of (x,x2) which produce at least output level yo.Econom...
(d) Let (x1,x) R..9x 2 yo} (3) S is the set of combinations of (x,x2) which produce at least output level yo.Economists refer to S'as the upper contour set associated with output yo. Assume that x (x,x2) S and y (y,y2) S. That is xfx yo and yy z yo. i) Let z (z1,z2) R.. What must be true for ze S? ( mark) ii) Let z= (z1,z2) x +(1A)y where 02<1 Prove that zE S Hint: Using results on...
Problem 3. (1) Let H be a Hilbert space and S, TE B(HH). Then, prove that...
Problem 3. (1) Let H be a Hilbert space and S, TE B(HH). Then, prove that ||ST|| ||||||||| (2) Let X, Y be Hilbert spaces and Te B(X,Y). Then, prove that ||1||| sup ||T3|1 TEX=1 Let X, Y be Banach spaces. Definition (review) We denote by B(X, Y) a set of all bounded linear operators T:X + Y with D(T) = X. B(X, Y) is a vector space. Definition (review) A linear operator T:X + Y is said to be...
1. If we had two 4-bit signed 2's complement numbers, X--4 and Y-6 and we wanted to compare them, we might calculate X-Y (a) Show that calculation (b) Explain how the result tells us that Y>IX...
1. If we had two 4-bit signed 2's complement numbers, X--4 and Y-6 and we wanted to compare them, we might calculate X-Y (a) Show that calculation (b) Explain how the result tells us that Y>IX (c) Now show the calculation for Y. X (d) Explain how this also shows us that Y>X 2. We talked about an ALU that takes two 4-bit inputs, A and B, and then generates a 4-bit result, S, based on a 2-bit command, F1FO....
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...
Topology
3. Either prove or disprove each of the following statements: (a) If d and p map (X, d) X, then the identity topologically equivalent metrics (X, p) and its inverse are both continuous are two on (b) Any totally bounded metric space is compact. (c) The open interval (-r/2, n/2) is homeomorphic to R (d) If X and Y are homeomorphic metric spaces, then X is complete if and only if Y is complete (e) Let X and Y...
10. Let T1 and T2 be two topologies on a set X. Then T1 is said to be a finer topology than T2 (and T2 is said to be a coarser topology than T1) if Ti2 T2. Prove that (i) the Euclidean topology R is finer than the finite-closed topology on R; (ii) the identity function f: (X, Ti) -(X, T2) is continuous if and only if TI is a finer topology than T2.
Have to get an idea of how i am doing on this problem. Whould be
nice to get a good explaination for each part of the problem. d1
and d2 is the two different metrics, p ,Y.
Problem 2. Consider first the following definition: Definition. Let X be a set and let pand be two metrics on X. We say that p and are equivalent if the open balls in (X, p) and (x,y) are "nested". More precisely, p and...
1. (a) Let d be a metric on a non-empty set X. Prove that each of the following are metrics on X: a a + i. d(1)(, y) = kd(x, y), where k >0; [3] ii. dr,y) d(2) (1, y) = [10] 1+ d(,y) The proof of the triangle inequality for d(2) boils down to showing b + > 1fc 1+a 1+b 1+c for all a, b, c > 0 with a +b > c. Proceed as follows to prove...
Problem 5. For u = (Uk)x=1,2,... El, we set Tnu = (U1, U2, ..., Un, 0,...). (1) Prove that Tn E B(C2, (). (2) We define the operator I as Iu = u (u € 14). Then, prove that for any u ele, lim ||T,u - Tulee = 0. (3) Prove that I, does not converge to I with respect to the norm of B(C²,1). Let X, Y be Banach spaces. Definition (review) We denote by B(X, Y) a set...
(d) Let (x1,x) R..9x 2 yo} (3) S is the set of combinations of (x,x2) which produce at least output level yo.Economists refer to S'as the upper contour set associated with output yo. Assume that x (x,x2) S and y (y,y2) S. That is xfx yo and yy z yo. i) Let z (z1,z2) R.. What must be true for ze S? ( mark) ii) Let z= (z1,z2) x +(1A)y where 02<1 Prove that zE S Hint: Using results on...
Problem 3. (1) Let H be a Hilbert space and S, TE B(HH). Then, prove that ||ST|| ||||||||| (2) Let X, Y be Hilbert spaces and Te B(X,Y). Then, prove that ||1||| sup ||T3|1 TEX=1 Let X, Y be Banach spaces. Definition (review) We denote by B(X, Y) a set of all bounded linear operators T:X + Y with D(T) = X. B(X, Y) is a vector space. Definition (review) A linear operator T:X + Y is said to be...
1. If we had two 4-bit signed 2's complement numbers, X--4 and Y-6 and we wanted to compare them, we might calculate X-Y (a) Show that calculation (b) Explain how the result tells us that Y>IX (c) Now show the calculation for Y. X (d) Explain how this also shows us that Y>X 2. We talked about an ALU that takes two 4-bit inputs, A and B, and then generates a 4-bit result, S, based on a 2-bit command, F1FO....
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...
Most questions answered within 3 hours.
-
Write an essay containing your thoughts on
whether corporations should be limited in the amount of...
asked 7 minutes ago -
A 4.0 L flask containing chlorine gas is connected to an
evacuated 3.0 L flask. If...
asked 6 minutes ago -
Given the following two sequences x (n)=[3 , 11,7 ,0 ,−1, 4 ,2
],−3≤n≤ 3 ;...
asked 7 minutes ago -
What is the minimal sample size needed for a 95% confidence
interval to have a maximal...
asked 8 minutes ago -
1. Methods of collecting data - Experiments and direct
observation
In each of the following situations,...
asked 22 minutes ago -
Each protein is composed of a maximum of ____________ different
amino acids in varying numbers and...
asked 39 minutes ago -
One member in the comp set that did not have supply, demand, and
revenue data. What...
asked 17 minutes ago -
What is the density of a substance that takes up 3.4e3 cubic cm
and weighs 1.96...
asked 32 minutes ago -
Consider a single wire loop of radius a. Calculate the magnetic
field B(z) along the axis...
asked 28 minutes ago -
For each of the compounds listed below you must draw the Lewis
dot structure in the...
asked 31 minutes ago -
1. Hypothesize in what type of environments it would be
advantageous for a protist to be...
asked 30 minutes ago -
The mayor of a town has proposed a plan for the construction of
a new community....
asked 49 minutes ago