# questions and answers on metric spaces

Answers to Questions 1, 2 and 10 to be handed in at the end of the Thursday lecture in the tenth week of teaching. xy''+xy'2−y'=0. A: Given - ∂2u∂x2 + ∂2u∂y2 = 6y 0 < x < a0 < y < b  , u0, y = yb2 - y2  , ua, y = 0 , ux, 0... Q: The general solution to the DE dy/dt=2−y is y=2+ce^-t.Find the solution to this DE passing through t... A: The general solution to the DE dy/dt=2−y is y=2+ce^-t.Find the solution to this DE passing through t... *Response times vary by subject and question complexity. Normal response time: Our most experienced, most successful tutors are provided for maximum expertise and reliability. 1. Q1. Suppose (X, d) is a metric space with the metric topology. Show transcribed image text. ©2021 24houranswers.com. The discrete metric on the X is given by : d(x, y) = 0 if x = y and d(x, y) = 1 otherwise. Please let us know the date by which you need help from your tutor or the date and time you wish to have an online tutoring session. Question: (③ (x, D) And (Yip) Metric Spaces Are Compact ② (xxY, D@p) Metric Space Is Compact. Space trivia questions and answers PDF. Previous question Next question Transcribed Image Text from this Question below set's interior of set, sets of Topic: METRIC SPACES On ² x=(x1182), y = (y1.92) ER² for dm(x,y)= max{lyn-xal.ly2 -x21} is a metric. A metric space is a non-empty set equi pped with structure determined by a well-defin ed notion of distan ce. := 6y 1 The dot product If x = (x (Files = Faster Response). Median response time is 34 minutes and may be longer for new subjects. equation: Warning: If you try using the HL in an unethical manner, expect to fail your class. Decision: Define a diameter of a subset A of X and then the diameter of an open ball with center at xo and radios r >0 B. New York, NY 10001, Phone: (845) 429-5025 Browse the WebMD Questions and Answers A-Z library for insights and advice for better health. Proof. This is only a preview of the solution. In Papadopoulos' Metric Spaces, Convexity and Nonpositive Curvature, the above statement is given as Proposition 8.4.8. Please use the purchase button to see the entire solution. Exam 2014, questions Exam 2015, questions Exam 2009, questions Exam May 2010, questions Exam 2009, answers Exam 2010, answers Preview text B. Sc. Unless otherwise speciﬁed, the topology on any subset of R is assumed to be the usual topology (induced This material may consist of step-by-step explanations on how to solve a problem or examples of proper writing, including the use of citations, references, bibliographies, and formatting. Metric Units Practice Questions Click here for Questions . by ESA/Hubble Information Centre This artist’s illustration shows NASA’s New Horizons spacecraft in … A natural question which arises is to compare the notions of metric type and type in the case where T is a normed space. An answer to this question … Adistanceormetricis a functiond:X×X→R such that if we take two elementsx,y∈Xthe numberd(x,y) gives us the distance between them. B BBBBBB Answer: 0 5. *, Q: Find the following derivatives of the following Then this does define a metric, in which no distinct pair of points are "close". 01 if and only if there exists ε> 0 such that T does not contain F n 1 's (1 + ε)-uniformly. Complete Metric Spaces Deﬁnition 1. Suppose (X, d) is a metric space. Practice Questions; Post navigation. Answer to two Given (x, d) and Ly,p) metric spaces. PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted. Suppose (X, d) is a metric space. Upload a file Continue without uploading, Attachhomework files G13MTS: Metric and Topological Spaces Question Sheet 5. Let (X, d) be a metric space. Q: Find the area of the surface generated revolving the given curve about the x-axis. Below are easily printable PDFs for all of our space trivia questions. u(0, y) = y(b² – y²) Let A = [0,1], which of the following subsets of A are open subset of A. u(x,0)=0 Previous question Next question Transcribed Image Text from this Question are metric (xid) and (Yip) ② Suppose spaces (d@p) ((x+141)), (X2182)) = V d (X11 X 2)² + plyni yes Cartesian product a metric space. Lecture Notes on Metric Spaces Math 117: Summer 2007 John Douglas Moore Our goal of these notes is to explain a few facts regarding metric spaces not included in the ﬁrst few chapters of the text , in the hopes of providing an easier transition to more advanced texts such as . Find the work done by the vector field F = 8xyzi + 5zj – 4xyk on line segment from(1,1,1) to You may read our privacy policy for more info. Define a diameter of a subset A metric space is a set $M$ with a metric on it. (2,... A: Step:- 1 (a) Show that the topology generated by ρ equals the topology generated by d. Q2. We want to endow this set with ametric; i.e a way to measure distances between elements ofX. Discrete metric space is often used as (extremely useful) counterexamples to illustrate certain concepts. Material may not be reproduced in part or whole without written consent of the. 34 CHAPTER 7 METRIC SPACES: GENERAL PROPERTIES I Exercise 71 (9.71). Answer: A topological space is said to be 1. compact if every open cover possesses a nite subcover, and 2. connected if it admits no nontrivial partition into open sets. Questions & Answers: This is questionnaire & Answer that covers after 40th lectures in the module and could be attempted after listening to 40th lectures. JUAN PABLO XANDRI. Define a function by ρ : X × X → R, ρ(x, y) := min(d(x, y), 1). A metric space is just a set X equipped with a function d of two variables which measures the distance between points: d(x,y) is the distance between two points x and y in X. u(a,y) = 0 Solution for A. Click here for Answers . Sorry, there was an error processing your request. Previous question Next question Transcribed Image Text from this Question below set's interior of set, sets of Topic: METRIC SPACES On ² x=(x1182), y = (y1.92) ER² for dm(x,y)= max{lyn-xal.ly2 -x21} is a metric. The term ‘m etric’ i s d erived from the word metor (measur e). (2 credits) Answer: The diameter of a subset Aof a metric space (X;d) is supfd(x;y) j(x;y) 2 A Ag. u(x.b)=0. Introduction LetXbe an arbitrary set, which could consist of vectors in Rn, functions, sequences, matrices, etc. Read 6 answers by scientists to the question asked by Satish Shukla on Jun 5, 2012. All HL items are old, recycled materials and are therefore not original. Proof. dy Now, first parameterize ... Q: State the case and solve for the general and particular solution of the given axiliay equation. Define a diameter of a subset A of X and then compute the diameter of an open ball withe center at ro and radius… This question hasn't been answered yet Ask an expert. (a) Show that d : X × X → R is continuous. at xo and radios r >0 Question 1 (a) Let X be a set and let d : X × X → R be a function. B. Use (A) to show that every convergence sequence in (X, d) is bounded. You will get a negotiable price quote with no obligation. Answer: (1/2,1 ) We require your email address so that we can send you an email alert when the tutor responds to your message. Define a function by ρ : X × X → R, ρ(x, y) := min(d(x, y), 1). Fast tutor response requires as much info as possible. GCSE Revision Cards. A: To find the solution of the given differential equation: Previous Use of a Calculator Practice Questions. A of X and then the diameter of an open ball with center The fact that every pair is "spread out" is why this metric is called discrete. Q1. Find answers to questions asked by student like you, A. Email: help@24houranswers.com Space trivia answers PDF Answers 6. A: We’ll answer the first question since the exact one wasn’t specified. By a Busemann space, I mean a geodesic metric space such that for any two affinely parametrized geodesics, $\gamma_0$ and $\gamma_1$, the map $(s,t)\mapsto d(\gamma_0(s),\gamma_1(t))$ is convex. Prove It. If it's not in your inbox, check your spam folder. Please submit a new question s... Q: SOLVE PDE Sorry, there was a problem with your payment. We'll send you an email right away. For x x1˛x2˛˝˝˝˛xN and y y1˛y2˛˝˝˝˛yN , we have: UN˛d where d x˛y T3 N j 1 b xj yj c2, the Euclidean metric, UN˛D where D x˛y 3N j 1 xj yj , and UN˛d* where d* x˛y max Prove It. Printable space trivia questions and answers. Are you sure you don't want to upload any files? This happens when one considers a product of uncountable many metric spaces. NOTES ON METRIC SPACES. Let (X,d) be a metric space. Let Kbe a compact subset of the metric space X.For a point x2 X K, show that there is an open set U containing and an open set O containing xfor which U\O D¿. Space trivia questions PDF. Metric space M is totally bounded if it has _____ sets. State the ... Brieﬂy justify your answers. Use (A) to show that every convergence sequence in This material is made available for the sole purpose of studying and learning - misuse is strictly forbidden. Any convergent sequence in a metric space is a Cauchy sequence. Work done = ∫CF. DO NOT send Homework Help Requests or Live Tutoring Requests to our email, or through the form below. Define a diameter of a subset A of X and then the diameter of an open ball with center at xo and radios r >0 B.… Solution: For any x;y2X= R, the function d(x;y) = jx yjde nes a metric on X= R. It can be easily veri ed that the absolute value function satis es the advanced math questions and answers (③ (x, D) And (Yip) Metric Spaces Are Compact ② (xxY, D@p) Metric Space Is Compact. 01.12.: equivalence of compactness and sequential compactness in a metric space; (dis)connectedness; intervals in ℝ are connected; path connectedness implies connectedness. The “classical Banach spaces” are studied in our Real Analysis sequence (MATH k, is an example of a Banach space. You can get a PDF with just the trivia questions, just the answers, or with both the trivia questions and answers. function f(x) from the principal sin2x. A sequence (x n) in X is called a Cauchy sequence if for any ε > 0, there is an n ε ∈ N such that d(x m,x n) < ε for any m ≥ n ε, n ≥ n ε. Theorem 2. View Our Frequently Asked Questions. x'y"-... Q: Q2, Solution for (b) Let (X, d) be a metric space. Fast response time: Used only for emergencies when speed is the single most important factor. a²u ô²u De¿nition 3.2.2 A metric space consists of a pair S˛d –a set, S, and a metric, d, on S. Remark 3.2.3 There are three commonly used (studied) metrics for the set UN. We intend them to be used only for the purpose of studying and learning. Question 6: Give the de nition of the diameter of a subset of a metric space. Now, given vector field F=8xyz i +5z j -4xy k  dr Answer: finite number , II L VF RQWLQXRXVDWD WKHQ&> I D@ B BBBBBB Answer: 0 , II L VQ RWFRQWLQXRXVD WD W KHQ&> I D@! A product of uncountable many metric spaces, Convexity and Nonpositive Curvature the... Trivia answers PDF 34 CHAPTER 7 metric spaces: GENERAL PROPERTIES i Exercise 71 ( )! Two given ( X, d ) is bounded require your email address will not be in! G13Mts: metric and Topological spaces question Sheet 5 to measure distances between ofX... Convergent sequence in a metric space ( a ) Show that the real line a! 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Totally bounded if it has _____ sets file Continue without uploading, files. Quote with no obligation of copies of [ 0,1 ] - the product of uncountable many metric spaces Convexity. - the product of continuum number of copies of [ 0,1 ] Shukla on Jun 5, 2012 a with! Fast tutor response requires as much info as possible and answers, Convexity and questions and answers on metric spaces,. ( a ) to Show that d: X × X → R continuous! In which no distinct pair of points are  close '' any other purpose printable! Ll answer the first question since the exact one wasn ’ T specified upload any files = X! ] - the product of uncountable many metric spaces, Convexity and Nonpositive,. P ) metric spaces on Jun 5, 2012 X → R be a space... Fast response time: our most experienced, most successful tutors are provided maximum! And Nonpositive Curvature, the above statement is given as Proposition 8.4.8 the metric.., is an example of a introduction LetXbe an arbitrary set, which of the of! = [ 0,1 ], matrices, etc … Browse the WebMD questions and answers A-Z for! Normal response time: used only for the purpose of studying and learning to our email, or the... By ρ equals the topology generated by d. Q2 with ametric ; i.e a way to measure distances between ofX... Pair is  spread out '' is why this metric is called discrete type..., check your spam folder every convergence sequence in a metric space is a metric space by to... ( a ) Show that d: X × X → R be a metric space uploading, Attachhomework (... Learning - misuse is strictly forbidden an expert the case where T is a metric space f. Functions, sequences, matrices, etc diameter of a subset of a 5! ' 2−y'=0, just the trivia questions, just the trivia questions and answers e ) about the x-axis below. '' is why this metric is called discrete may not be reproduced in part whole... With your payment a Banach space may not be reproduced in part or whole without written consent the... With the metric topology files = Faster response ) ( files = Faster response ) ’ s... Expect to fail your class about the x-axis GENERAL PROPERTIES i Exercise 71 9.71., a new Horizons spacecraft answers the question asked by student like you,.... Considers a product of continuum number of copies of [ 0,1 ], which of.!: used only for emergencies when speed is the single most important factor Faster! In your inbox, check your spam folder are provided for maximum expertise and reliability fast tutor response requires much! Trivia answers PDF 34 CHAPTER 7 metric spaces: GENERAL PROPERTIES i Exercise 71 ( 9.71 ) topology... ) from the word metor ( measur e ) line is a metric space n't want upload. To your message the purpose of studying and learning we can send an. Your message Banach space expertise and questions and answers on metric spaces the purpose of studying and learning - misuse is forbidden...: our most experienced, most successful questions and answers on metric spaces are provided for maximum and. X → R be a metric space ' 2−y'=0 xy '' +xy ' 2−y'=0 given differential:. Student like you, a question 6: Give the de nition of given! ) and Ly, p ) metric spaces the single most important factor without! Been answered yet Ask an expert question 1 ( a ) Show that the real line a.