Q3: state whether the following statement are True or False : 6. In Euclidean space R the ball B(0; 1) is the open interval (-1,1) and in the metric [0,1] of R the ball B, (0; 1) is the half-open interval [0,1). n": n E N} is an open set . subspace S = sin nл 7. The set S= 8. If A = [-2,0) and B = (0,8] and C = {x + y: x E A, y € B} then Inf C = 2. 9. The set of all interior points for the set of real numbers is R. 10. The open ball in R3 is an open circular disk.
Q3: state whether the following statement are True or False : 6. In Euclidean space R the ball B(0; 1) is the open interval (-1,1) and in the metric [0,1] of R the ball B, (0; 1) is the half-open interval [0,1). n": n E N} is an open set . subspace S = sin nл 7. The set S= 8. If A = [-2,0) and B = (0,8] and C = {x + y: x E A, y € B} then Inf C = 2. 9. The set of all interior points for the set of real numbers is R. 10. The open ball in R3 is an open circular disk.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.3: Subspaces Of Vector Spaces
Problem 49E
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![Q3: state whether the following statement are True or False :
6. In Euclidean space R the ball B(0; 1) is the open interval (-1,1) and in the metric
[0,1] of R the ball B, (0; 1) is the half-open interval [0,1).
subspace S
-
sin nπ
7. The set S =
:n EN is an open set.
:neN}
2
8. If A = [-2,0) and B = (0,8] and C = {x + y: x E A, y E B} then Inf C = 2.
9. The set of all interior points for the set of real numbers is R.
10. The open ball in R3 is an open circular disk.
ا فاي بارد **
Shaugen I Abbas](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F42523a8a-9780-4126-b7bf-7a8dfe68a620%2Fe6bdb2c0-8fdc-46e0-99b0-90c3e4b69790%2F66n9jx9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Q3: state whether the following statement are True or False :
6. In Euclidean space R the ball B(0; 1) is the open interval (-1,1) and in the metric
[0,1] of R the ball B, (0; 1) is the half-open interval [0,1).
subspace S
-
sin nπ
7. The set S =
:n EN is an open set.
:neN}
2
8. If A = [-2,0) and B = (0,8] and C = {x + y: x E A, y E B} then Inf C = 2.
9. The set of all interior points for the set of real numbers is R.
10. The open ball in R3 is an open circular disk.
ا فاي بارد **
Shaugen I Abbas
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