7. Suppose that a set X is equipped with the finite closed topology. Which one of the followings is true. a. VACX, A=X b. the only subsets of X which are open and closed are X and c. the closed subsets of X are not necessarily finite d. X is not necessarily connected
7. Suppose that a set X is equipped with the finite closed topology. Which one of the followings is true. a. VACX, A=X b. the only subsets of X which are open and closed are X and c. the closed subsets of X are not necessarily finite d. X is not necessarily connected
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![8:03 A
46 ll 90% i
7. Suppose that a set X is equippod with the finite elosed topology. Which one of the followings is
true
a. VAC X, A = X
b. the only subsets of X which are open and closed are X and o
c. the closed subsets of X are not necessarilv finite
d. X is not necessarily connceted
a
7. Let X = R? equipped with the usual metric do. Which of the following is true
(a) (X, do) is complete but not compact
(b) (X, do) is compact but not complete
(c) (X, do) is complete and compact
(d) (X, do) is neither complete nor compact
a
K](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F34109864-7571-4d0f-b6bb-13697d446880%2Fca2a2a59-e21d-4678-8066-88753756e7fb%2F9v89hrg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:8:03 A
46 ll 90% i
7. Suppose that a set X is equippod with the finite elosed topology. Which one of the followings is
true
a. VAC X, A = X
b. the only subsets of X which are open and closed are X and o
c. the closed subsets of X are not necessarilv finite
d. X is not necessarily connceted
a
7. Let X = R? equipped with the usual metric do. Which of the following is true
(a) (X, do) is complete but not compact
(b) (X, do) is compact but not complete
(c) (X, do) is complete and compact
(d) (X, do) is neither complete nor compact
a
K
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