Question

1. Consider the set U={(x,y) in R2| -1<x<1 and y=0}. Is U open in R2? Is...

1. Consider the set U={(x,y) in R2| -1<x<1 and y=0}. Is U open in R2? Is it open in R1? Is it open as a subspace of the disk D={(x,y) in R2 | x^2+y^2<1} ?

2. Is there any subset of the plane in which a single point set is open in the subspace topology?

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Exercise 9.1.11 Consider the set of all vectors in R2,(x, y) such that x + y...
Exercise 9.1.11 Consider the set of all vectors in R2,(x, y) such that x + y ≥ 0. Let the vector space operations be the usual ones. Is this a vector space? Is it a subspace of R2? Exercise 9.1.12 Consider the vectors in R2,(x, y) such that xy = 0. Is this a subspace of R2? Is it a vector space? The addition and scalar multiplication are the usual operations.
Determine if the subset W={[x y]∈R2∣ x+y ≥0} is a subspace of R2.
Determine if the subset W={[x y]∈R2∣ x+y ≥0} is a subspace of R2.
topology: Prove that the open ball B2: = {(x, y) ∈ R2 | x2 + y2...
topology: Prove that the open ball B2: = {(x, y) ∈ R2 | x2 + y2 <1} in R2 is homeomorphic to the open squared unit C2: = {(x, y) ∈R2 | 0 <x <1.0 <and <1}
Prove that the open rectangle in R2     S = { (x,y) | 2 < x<5 -8...
Prove that the open rectangle in R2     S = { (x,y) | 2 < x<5 -8 < y < -1} is an open set in R2, with the usual Euclidean distance metric.
Let U = Z+ ∪ { 0 }. Let R1 = { ( x, y )...
Let U = Z+ ∪ { 0 }. Let R1 = { ( x, y ) | x ≠ y } Let R2 = { ( x, y ) | x = y } Let R3 = { ( x, y ) | x ≥ y } Let R4 = { ( x, y ) | x ≤ y } Let R5 = { ( x, y ) | x > y } Let R6 = { ( x, y...
On set R2 define ∼ by writing(a,b)∼(u,v)⇔ 2a−b = 2u−v. Prove that∼is an equivalence relation on...
On set R2 define ∼ by writing(a,b)∼(u,v)⇔ 2a−b = 2u−v. Prove that∼is an equivalence relation on R2 In the previous problem: (1) Describe [(1,1)]∼. (That is formulate a statement P(x,y) such that [(1,1)]∼ = {(x,y) ∈ R2 | P(x,y)}.) (2) Describe [(a, b)]∼ for any given point (a, b). (3) Plot sets [(1,1)]∼ and [(0,0)]∼ in R2.
Consider the following subset: W =(x, y, z) ∈ R^3; z = 2x - y from...
Consider the following subset: W =(x, y, z) ∈ R^3; z = 2x - y from R^3. Of the following statements, only one is true. Which? (1) W is not a subspace of R^3 (2) W is a subspace of R^3 and {(1, 0, 2), (0, 1, −1)} is a base of W (3) W is a subspace of R^3 and {(1, 0, 2), (1, 1, −3)} is a base of W (4) W is a subspace of R^3 and...
Verify this axiom of a vector space. Vector space: A subspace of R2: the set of...
Verify this axiom of a vector space. Vector space: A subspace of R2: the set of all dimension-2 vectors [x; y] whose entries x and y are odd integers. Axiom 1: The sum u + v is in V.
(a) This exercise will give an example of a connected space which is not locally connected....
(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...
1. Consider the following situation: The universal set U is given by: U = {?|? ?...
1. Consider the following situation: The universal set U is given by: U = {?|? ? ? , ? ≤ 12} A is a proper subset of U, with those numbers that are divisible by 4. B is a proper subset of U, with those numbers that are divisible by 3. C is a proper subset of U, with those numbers that are divisible by 2 a) Using Roster Notation, list the elements of sets U, A, B and C....
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT