Question
Asked Sep 18, 2019
1 views

Suppose M is an n-manifold with boundary. Show that ∂M with the subspace topology is an n − 1-manifold (without boundary). You may use that interior(M) ∩ ∂M = ∅. (∂M is the boundary of M).

check_circle

Expert Answer

Step 1

To prove that the boundary of a n-manifold is a (n-1) manifold without boundary

Step 2

As the question is purely local , we may take the n-manifold M to be the closed unit disk in R^n.

Step 3

The unit sphere is a manifold (without boundary): we can use the atlas provided by the two open sets after removing t...

help_outline

Image Transcriptionclose

So,let M closed unit disk in R" {x: xeR":1} In this case , boundary of M ôM = {x: x e R" :|| |= 1} (fhe unit sphere), which is a manifold of dim ension n-1

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Advanced Math

Related Advanced Math Q&A

Find answers to questions asked by student like you
Show more Q&A
add
question_answer

Q: Differential equations Find the particular solution to the initial value problem: (x+2)y"+xy'-y=0,  ...

A: Consider the differential equation.

question_answer

Q: 5.4 the book is "First Course on Fuzzy Theory and Applications" please, I need the solution of part ...

A: Consider the following given fuzzy sets:

question_answer

Q: Can you add more pictures space? See at the bottom question picture.

A: The function is given by,

question_answer

Q: 7. Find f(4) if f is defined recursively by f(0) = 2, f(1) = 3 and f(n+ 1) 4f(n) -3f(n-1)

A: To find: The value of f (4).Given: The recursive function is defined as

question_answer

Q: Mechanical Vibrations (differential equations) A mass weighing 4 pounds is attached to a sping whose...

A: Let m be the mass attached, k be the spring constant and let b be a positive damping constant.Then, ...

question_answer

Q: 27+2548+432+9=?

A: Given that the expression is

question_answer

Q: Perform the following calculations to the correct number of significant figures. [(2.81×106)÷42.170]...

A: Calculation:Perform the calculation to the correct number of significant figures as follows.[(2.81×1...

question_answer

Q: In group theory (abstract algebra), is there a special name given either to the group, or the elemen...

A: Yes, there is a special name given either to the group, or the elements themselves, if x2=e for all ...

question_answer

Q: 3-7. Write each answer with the correct number of significant figures (a) 1.02.1 + 3.4 + 5.8 12.300 ...

A: As per the norm, the first three questions are answered.  Problem: To express the result of operatio...