Question

Assume that a and b are two continuous injective maps with a(0)=(-1,0), a(1)=(1,0), b(0)=(0,-1) and b(1)=(0,1)....

Assume that a and b are two continuous injective maps with a(0)=(-1,0), a(1)=(1,0), b(0)=(0,-1) and b(1)=(0,1). Show that the curves a and b must intersect

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
Show that a continuous injective map f: (0, 1) to R is an embedding.
Show that a continuous injective map f: (0, 1) to R is an embedding.
show 1/(x^1/2) is not uniformly continuous on the interval (0,1).
show 1/(x^1/2) is not uniformly continuous on the interval (0,1).
Show there does not exist a sequence of continuous functions fn : [0,1] → R converging...
Show there does not exist a sequence of continuous functions fn : [0,1] → R converging pointwise to the function f : [0,1] → R given by f(x) = 0 for x rational, f(x) = 1 for x irrational.
Determine whether the set of all continuous functions on [0,1] satisfying f(0) = 1 constitutes a...
Determine whether the set of all continuous functions on [0,1] satisfying f(0) = 1 constitutes a real linear space under the usual operations associated with elements of the set.
Let X=2N={x=(x1,x2,…):xi∈{0,1}} and define d(x,y)=2∑(i≥1)(3^−i)*|xi−yi|. Define f:X→[0,1] by f(x)=d(0,x), where 0=(0,0,0,…). Prove that maps X onto...
Let X=2N={x=(x1,x2,…):xi∈{0,1}} and define d(x,y)=2∑(i≥1)(3^−i)*|xi−yi|. Define f:X→[0,1] by f(x)=d(0,x), where 0=(0,0,0,…). Prove that maps X onto the Cantor set and satisfies (1/3)*d(x,y)≤|f(x)−f(y)|≤d(x,y) for x,y∈2N.
Let C [0,1] be the set of all continuous functions from [0,1] to R. For any...
Let C [0,1] be the set of all continuous functions from [0,1] to R. For any f,g ∈ C[0,1] define dsup(f,g) = maxxE[0,1] |f(x)−g(x)| and d1(f,g) = ∫10 |f(x)−g(x)| dx. a) Prove that for any n≥1, one can find n points in C[0,1] such that, in dsup metric, the distance between any two points is equal to 1. b) Can one find 100 points in C[0,1] such that, in d1 metric, the distance between any two points is equal to...
(a) Show that the function g: (0,1)→(0,∞)with g(x) =(1−x)/x is a bijection (b)Show that the natural...
(a) Show that the function g: (0,1)→(0,∞)with g(x) =(1−x)/x is a bijection (b)Show that the natural logarithm ln: (0,∞)→R is a bijection (c) Show that R has the same cardinality as the interval (0,1)
Let B be the set of all binary strings of length 2; i.e. B={ (0,0), (0,1),...
Let B be the set of all binary strings of length 2; i.e. B={ (0,0), (0,1), (1,0), (1,1)}. Define the addition and multiplication as coordinate-wise addition and multiplication modulo 2. It turns out that B becomes a Boolean algebra under those two operations. Show that B under addition is a group but B under multiplication is not a group. Coordinate-wise addition and multiplication modulo 2 means (a,b)+(c,d)=(a+c, b+d), (a,b)(c,d)=(ac, bd), in addition to the fact that 1+1=0.
Consider the linear map ? : R2 → R2 which sends (1,0) ↦→ (−3,5) and (0,1)...
Consider the linear map ? : R2 → R2 which sends (1,0) ↦→ (−3,5) and (0,1) ↦→ (4, −1). (a) What is the matrix of the transformation? What is the change of coordinates matrix? Do they agree? How come? ( Please compute both the matrix of the transformation and the change of coordinates matrix!) (b) Where does this transformation send the area between the vector (4, 2) and the x-axis? Explain algebraically and draw a picture. (c) What is the...
Let X be a continuous random variable with a PDF of the form fX(x)={c(1−x),0,if x∈[0,1],otherwise. c=...
Let X be a continuous random variable with a PDF of the form fX(x)={c(1−x),0,if x∈[0,1],otherwise. c= P(X=1/2)= P(X∈{1/k:k integer, k≥2})= P(X≤1/2)=
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT