The 1st part is true for more than one metric spaces one such example is this one
But incase of R with usual metric d that is d(x,y) =|x-y| this statement is not true a thorough proof is given below
Hope it helps :-)
11) Give an example to show that the following can happen in a metric space: Brı...
(a) This exercise will give an example of a connected space which is not locally connected. In the plane R2 , let X0 = [0, 1] × {0}, Y0 = {0} × [0, 1], and for each n ∈ N, let Yn = {1/n} × [0,1]. Let Y = X0 ∪ (S∞ n=0 Yn). as a subspace of R 2 with its usual topology. Prove that Y is connected but not locally connected. (Note that this example also shows that...
Problem 3 (LrTrmations). (a) Give an example of a fuction R R such that: f(Ax)-Af(x), for all x € R2,AG R, but is not a linear transformation. (b) Show that a linear transformation VWfrom a one dimensional vector space V is com- pletely determined by a scalar A (e) Let V-UUbe a direet sum of the vector subspaces U and Ug and, U2 be two linear transformations. Show that V → W defined by f(m + u2)-f1(ul) + f2(u2) is...
I have done the a and b, but i'm so confuse with other questions, could someone help me to fix these questions, thanks so much. 4 Directed graphs Directed graphs are sometimes used operating systems when trying to avoid deadlock, which is a condition when several processes are waiting for a resource to become available, but this wil never happen because Page 2 p2 T2 Figure 1: Minimal example of a resource allocation graph with deadlock other processes are holding...
Please show working and explanation if possible. Thank you so much in advance! The first four spherical harmonics Ym are given below. r-e'a cose 3 11/2 Y. 3 11/2 3 1/2 sin θ e_ίφ a) Give the mathematical functions that describe the s orbital and the pz orbital. (10 marks) b) Unsöld's theorem states that the spherical harmonics satisfy the relation +I IYİm12 = constant m--l t Unsöld's theorem is valid for the family of spherical harmonics with (15 marks)...
Hi, could you post solutions to the following questions. Thanks. 2. (a) Let V be a vector space on R. Give the definition of a subspace W of V 2% (b) For each of the following subsets of IR3 state whether they are subepaces of R3 or not by clearly explaining your answer. 2% 2% (c) Consider the map F : R2 → R3 defined by for any z = (zi,Z2) E R2. 3% 3% 3% 3% i. Show that...
Please use Excel, and show all functions. 3. Answer the following question for where Y has been regressed on X1, X2, and X3. Use the linear regression output in the Excel file. Your answers should be rounded to 2 decimal places. a. What is the equation for the line of best fit or regression line? b. The proportion is for the amount of the variability of Y that is explained or accounted for by the model. C. The correlation between...
please answer the following using the r code provided . The data set below contains information about the gasoline mileage performance for 32 au- tomobiles. We are interested in developing a model to predict the miles per gallon () using related predictor variables. The variables in the study are Dependent variable: Miles per gallon (v) Independent variables: ri horsepower (ft-lb) ra: torque (ft-lb) r: horsepower+torque (ft-lb) rs: carburetor (barrels) (a) We first start by fitting a model using y and...
Please show all work in the space provided for credit. 1.) The function D(h) 10e can be used to find the number of milligrams D of a certain a. How many milligrams will be present after 2 hours? b. When the number of milligrams reaches 1, the drug is to be administered again. drug that is in a patient's bloodstream h hours after the drug has been administered Round your answer to one decimal place. After how many hours will...
PART A 21 MARKS SHORT ANSWER QUESTIONS Answer ALL questions from this part. Write your answers in the Examination Answer Booklet. Each question is worth 1.5 marks (14 x 1.5 = 21 marks). Question 1 An organisation has been granted a block of addresses with the mask /22. If the organisation creates 8 equal-sized subnets, how many addresses (including the special addresses) are available in each subnet? Show your calculations. Question 2 Give an example of a valid classful address...
A group of physics students collected data from a test of the projectile motion problem that was analyzed in a previous lab exercise (L5). In their test, the students varied the angle and initial velocity Vo at which the projectile was launched, and then measured the resulting time of flight (tright). Note that tright was the dependent variable, while and Vo were independent variables. The results are listed below. (degrees) Time of Flight (s) Initial Velocity V. (m/s) 15 20...