Answered: Let (N, d) be the discrete metric…

Let (N, d) be the discrete metric space, then the set A = {2,3, 4} is closed but not open open but not closed O neither open nor closed O open and closed O

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CM: Cumulative Review

Problem 24CM

See similar textbooks

Related questions

Q: If τ1 = {A ⊂ X : p ∈ A} ∪ {∅} is a topology on X, then determine whether (X, τ1) is a normal space…

A: τ1 = {A ⊂ X : p ∈ A} ∪ {∅} is a topology on X, then determine whether (X, τ1) is a normalspace or…

Q: Let X = [0, 1] U [2, 3] endowed with the standard metric. Then [0, 1] is an open subset of X. Select…

Q: Let (X, d) be a metric space and let A ⊆ X be a compact subset. show that, If B ⊆ X and d(A, B) =…

Q: Let (N, d) be the usual metric space, then the set A= {1,3} is O closed only O neither open nor…

A: ( N,d) be a usual metric space of natural number. A={1,3} be a finite subset of N. Since A is…

Q: The only subsets of R which are both open and closed under the discrete metric are Ø and R. Select…

A: This is False statement, in discreate metric space, every subset of R is both open as well as…

Q: Let R be the usual space * In R, if A = [-4,0) U N, then A' = ON O [-4,0] U N O [-4,0) O [-4,0]

Q: Let (R. d) be discrete metric space then R is not complete O True O Faise

Q: Let E be a subset of X, where X is a metric space. Show the limit points of E are the same as the…

A: In mathematics, the closure of a subset S of points in a topological space consists of all points in…

Q: (b) Prove that the set S = {x EQ: √2<x<√3} is closed and bounded in (Q.1-1), but not compact in…

Q: Lemma 2.56 Let (X,T) be a topological space, (M, d) be a complete metric space and BC(X, M) := {f e…

Q: Let (X,T) be a separable topological space, let A be an open subset of X. Then (A, T,) is a…

Q: Let (R. d) be discrete metric space, thend can not induces a norm on X O True O Fahe

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 5. Let (X, d) be a metric space. i) Show that the open ball B, (ro) = {x € X : d (T, xo) < r} is an…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Let (X,t) be a topological space, A, B C X. Then A' UB' = (A U B)', A'n B' c (A N B)' Select one: O…

Q: Consider IR as a metric space.with metric dux, y) = 1x-y1. Show that the open interval C0, 1) is an…

Q: If S is a closed bounded subset of a metric space X, then S is compact.

Q: Let

Q: Let A and B be any two subsets of a metric space (X, d). Then (1) A is a closed set. (2) If AC B,…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 5. Let (X,T) be a discrete space, then Va E X, the set {a} is а. ореn b. closed c. clopen d. is…

A: Let (X, T) be a discrete space.

Q: Let X be a discrete spaces then O X is homeomorphic to R if and. only if X is countable O X is…

A: I have provided a solution in step2

Q: Let (X, T) be a topological space and A, B be a subsets of X then: اختر احدى الدجابات int(A - B)=…

Q: let Qid) be a metric space and AiB Bubeet of x ACB = d(A) cd(B) [ Soi d(A) is closed set] P B is…

A: Let X,d be a metric space and A, B⊆X. We will use the following in the proofs, Definition of clA:…

Q: Let (X,d) be a metric space , x ϵ X and A ⊑ X be a nonempy set. Prove that d (x ,A) = 0 if and only…

A: Given: X,d is a metric space, x∈X and A⊂ X is a non-empty set. To Prove: dx,A=0 if and only if every…

Q: 5. Let X be a set and p E X. b) If 72 = {A C X : p ¢ A}U{X}is a topology on X, then determine…

Q: Exercise. Prove that in a metric space (X, p), a set G C X is open if and only if it is a union of…

Q: let C be a compact subset in a Hausdorff topological space (X,T) and b∈X a point. If b∉C then prove…

Q: X is not open, must it be closed? Either prove that every subset E that is not open must be closed,…

A: We will show it by giving example

Q: Let (X, d) be a metric space. a) Assume that A is a (finite or infinite) collection of open sets.…

A: To orove the required topological properties of open sets in a metric space (X,d)

Q: Let (X,T) be a topological space such that every subset of X is closed, then a. (X,T) is an…

A: (X,T) is a topological space such that every subset of X is closed

Q: Let (C[a,b] .d) be the discrete metric space. Then Cla,b] is bounded. * False True

Q: If A is a subset of a metric space X, then show that A = (x: each neighbourhood of x intersects A}

Q: A of a metric space (x, d.)

Q: 1. Let M, d be a metric space with A C B C M. Suppose that B is totally bounded. Prove that A is…

A: Let (M, d) be a metric space and let A be a nonempty subset of M. The diameter of A is defined as…

Q: Exercise. Prove that in a metric space (X,p), a set G CX is open if and only if it is a union of…

Q: Let X be a set with more than one element. (X,7) is a topological space such that Vxe X, {x} €T then…

A: Given the set X contains more than one element.

Q: Q2: In Euclidean metric space (R2, 1. 1), is the set A = {(x, y): 2x² + y² = 1} compact? giving the…

Q: Every closed subset of a connected metric space is connected. O True O False

Q: 5. Let (X,T) be a discrete space, then Va E X, the set {a} is а. орen b. closed c. clopen d. is…

A: Our objective is to choose the correct choice

Q: the following subsets in an indicated metric space determine the interior, boundary points and…

A: Ans:

Q: Prove that in a metric space (X, d) every closed ball that is a set K(x, r) = {y e X : d(x, y) <=…

A: Question: Prove that in a metric space X, d every closed ball K¯x, r=y∈X, dx, y≤r is a closed set.…

Q: Let (R, d) be the metric space with d(x, y) = /[x – y[. Then the open ball O [-3, 5] ]-3, 5[ ]-1, 3[…

Q: A topological space (X, t) is a T1-space if and only il for each x e X, the singleton set {x} is…

Q: 5. State whether the following is true or false m) A subset I of a metric space R with the usual…

Q: 5. Let (X,7) be a discrete space, then Va E X, the set (a} is a. open b. closed c. clopen d. is…

A: As per our guidelines we are suppose to answer onlyone question, kindly post the other questions as…

Q: 2) Let A be a closed bounded subset of a metric space (X, d). Is A a compact subset? Explain why.

Q: Let X be a metric space. Let A and B be separated sets in X. Show either E is a subset of A or E is…

Q: Exercise. Prove that in a metric space (X, p), a set GC X is open if and only if it is a union of…

A: Solution

Question

Let (N, d) be the discrete metric space, then the set A = {2, 3, 4} is
closed but not open
open but not closed O
neither open nor closed O
open and closed O

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Complexity$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

27. Let , where and are nonempty. Prove that has the property that for every subset of if and only if is one-to-one. (Compare with Exercise 15 b.). 15. b. For the mapping , show that if , then .
Let f:AA, where A is nonempty. Prove that f a has right inverse if and only if f(f1(T))=T for every subset T of A.
Suppose thatis an onto mapping from to. Prove that if ℒ, is a partition of, then ℒ, is a partition of.
Suppose f,g and h are all mappings of a set A into itself. a. Prove that if g is onto and fg=hg, then f=h. b. Prove that if f is one-to-one and fg=fh, then g=h.
Let (X, d) be a metric space and let A be a non-empty subset of X. Prove that A is open if and only if it can be written as the union of a family of open balls of the form Br(x) = {y ∈ X : d(x, y) < r}.
Let E1, E2, ..., En ⊂ X,d be compact subsets of a metric space X. Just using the definition of compactness, prove that E1 ⋃ E2, ⋃ ... ⋃ En, where n is a postive integer, is a compact subset of X.
Let (X,d) be a metric space , x ϵ X and A ⊑ X be a nonempy set. Prove that d (x ,A) = 0 if and only if every neighborhood of x contains a point of A.
Let M1 and M2 be two metric spaces and let A is a subset of M1. If f: M1→M2 is continuous, show that f|A: A→M2 is also continuous
Let A be a subset of a complete metric space. Assume that for all ε > 0, there exists a compact set Aε so that ∀x ∈ A, d(x, Aε) < ε. Show that A (close) is compact.
Let (X, d) be a metric space and let A ⊆ X be complete. Show that A is closed.
If E is a subset of a metric space (X, d), show that E is nowhere-dense in X if and only if E c is dense in X.
Let X be a metric space. Let A and B be separated sets in X. Show either E is a subset of A or E is a subset of B where E is a connected subset of A U B.