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
A bag contains 13 red bulbs,5 white bulbs and some green bulbs. a bulb is selected at random from the bag. the probability of se
maw [93]
1. There are 6 green bulbs because
13+5=18*1/3=6 green bulbs
2. The probability of getting a red bulb is 15/8
Hope it helps you!!!!
4 0
3 years ago
In a recent
qwelly [4]

Answer:collecting data

Step-by-step explanation:

7 0
2 years ago
If a 35 ft rope is cut into two sections with one section 6 times as long as the other section, how long is the shorter piece?
Yuliya22 [10]
The smallest piece is 5ft, 5x6+5=35 
4 0
3 years ago
Read 2 more answers
Give 3 pairs of prime numbers that add up to 50
aleksley [76]

Answer:

3 and 47

7 and 43

19 and 31

Step-by-step explanation:

Prime numbers up to 50:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47

Therefore,

3 + 47 = 50

7 + 43 = 50

19 + 31 = 50

7 0
2 years ago
I’ll give Brainly but pleaseee help
77julia77 [94]
Fruit adult = 26
fruit total = 52
vegetable child = 14
total child = 40
total adult = 50
8 0
3 years ago
Other questions:
  • Plz help will mark brainliest ....Given f(x)=5x2−2x and g(x)=3x2+x−4 .
    7·2 answers
  • Solve for n: -4 (3n+3) = 5 (-2-6n) -2
    13·2 answers
  • true or false the shortest distance from the center of the circumscribed circle to the sides of the inscribed triangle is the ci
    14·2 answers
  • 6xy-8x2 what is the answer to this question
    7·2 answers
  • Miguel baked 40 cookies with 8 ounces of chocolate chips. How many cookies could he bake with one ounce of chocolate chips ?
    6·1 answer
  • A $3,000 loan is taken out for 9% interest for 6 months. What is the amount of interest charged?
    11·2 answers
  • What are two possible transformations that together could have been used to create the red figure from the blue figure?
    10·2 answers
  • 36.95-36.95+59.72?????
    12·2 answers
  • Simplify the expression
    13·1 answer
  • What is one solution of the following system?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!