1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Alex_Xolod [135]
3 years ago
7

If S is a compact subset of R and T is a closed subset of S, then T is compact. Prove this using the definition of compactness.

Mathematics
1 answer:
wlad13 [49]3 years ago
3 0

Answer:

It has been proved that T is compact

Step-by-step explanation:

To prove this using the definition of compactness, let's assume that T is

not compact. Now, if that be the case, an open cover of T will exist. Let's call this open cover "A". Now, this open cover will have no finite subcover.

Now, from the question, since T is closed, it’s complement R\T will be open.

Therefore, if we add the set R\T to the collection of sets A, then we'll have an open cover of R and also of S.

Due to the fact that S is compact, this

cover will have a finite sub - cover which we will call B.

Finally, either B itself or B\{R\T} would be a finite sub - cover of A. This is a contradiction.

Thus, it proves that T has to be compact if S is to be a compact subset of R and T is to be a closed subset of S.

You might be interested in
In a 60 sheet package of construction paper there are 15 yellow sheets what is the probability that a randomly selected sheet wi
Free_Kalibri [48]

Answer:

15/60 or 1/4, which is 25%

Step-by-step explanation:

5 0
3 years ago
How do I find an implied domain?
Ira Lisetskai [31]

Answer:

https://youtu.be/GQGFMUfr10M

OPEN THE LINK SHARED ABOVE

I HOPE MY ANSWER HAS HELPED YOU :)

3 0
3 years ago
Question 1 - work out the value of 300
MAXImum [283]

question 1=30

question 3 =1/20

Step-by-step explanation:

question 1

  1. 300/2×5
  2. 300/10
  • 300\10 you will take by 0 0
  • so the ans is 30/1
  • answer is 30

question 2 am not sure

question 3

  • it is 20/1
  • so the reciprovol of 20/1 is 1/20
  • that's all I know for no 2 I will some one. thanks
4 0
3 years ago
Read 2 more answers
Find the surface area of the shape.
Firlakuza [10]

Answer:

268 m²

Step-by-step explanation:

8x26=208

3x10x2=60

208+60=268

7 0
3 years ago
Graph these equations:<br> x + 3y = 6<br> x + 3y = 9
Evgen [1.6K]
I don’t know if you can see this but I hope it does if u don’t understand let me know so I can explain!

6 0
2 years ago
Other questions:
  • How many terms are in the algebraic expression 3x2 + 4y - 1?<br> A. 2<br> B. 3<br> C. 5 <br> D. 4
    11·2 answers
  • If a worker is paid $8.16 per hour and works 8.5 hours in one week, how much is he or she paid for that week? A. $65.68 B. $65.2
    15·2 answers
  • Each person in a large square occupies, on average, 2.5 sq. feet of space. Estimate the number of people that can comfortably st
    10·2 answers
  • Simplify the variable expression by evaluating its numerical part, and enter
    10·1 answer
  • The speed of a fish before jumping out of the water can be represented by the equation s = 3h, where h
    14·1 answer
  • Algebra 1 brainilest if correct and reported if not answered.
    7·1 answer
  • House Prices
    8·2 answers
  • (x+y,x-y)=(8,0) find the value of x and y​
    14·1 answer
  • Hehehejejwjjejejjejejwkwkwkekekejjeue
    6·1 answer
  • Select all the expressions that are equivalent to 4 x 4 x 4 x 4 x 4
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!