Topics

General Knowledge
General Science
General English
Aptitude
General Computer Science
General Intellingence and Reasoning
Current Affairs
Exams
Elementary Mathematics
English Literature

Compact implies

A) bounded only
B) closed only
C) closed and bounded
D) none of these

Correct Answer:



C) closed and bounded

Part of solved Real Analysis questions and answers : >> Elementary Mathematics >> Real Analysis

Comments

Similar Questions

1). In Euclidean space \(R^{k}\) every cauchy sequence is

A). convergent

B). divergent

C). bounded

D). none of these

-- View Answer

2). The set s of intervals with rational end points is a

A). countable set

B). uncountable set

C). bounded set

D). none of these

-- View Answer

3). The union of finite collection of closed sets is

A). bounded

B). open

C). closed

D). none of these

-- View Answer

4). Find the sup and inf of the set A = {-1, -2, -3,...}

A). sup = -1; inf \(\in\)A

B). sup \(\in\)A; inf = -1

C). sup = -1; inf = -2

D). none of these

-- View Answer

5). Find thegvalues of x which satisfy the inequality \(|4-5x|\le 6\)

A). numbers in the open interval \(\Large \left(\frac{-2}{5},2\right) \)

B). numbers in the closed interval \(\Large \left(\frac{-2}{5},2\right) \)

C). numbers in the closed interval [0, 1]

D). none of these

-- View Answer

6). Find the values of x which satisfy inequality |3x-2| > 5

A). x lies inside the interval \( \left(-1,\frac{7}{3}\right) \)

B). x lies outside the interval \( \left(-1,\frac{7}{3}\right) \)

C). x lies inside the interval \( \left(+1,\frac{-7}{3}\right) \)

D). none of these

-- View Answer

7). Find the lub and glb of sets \(\Large \{ 1-\frac{1}{n};\ n\in N \}\)

A). lub = 1; glb = 0

B). lub = 0; glb = 1

C). lub = -1; glb = 1

D). none of these

-- View Answer

8). \(\Large \{ \frac{1}{5n}:n\in Z| n\ne 0 \}\)

A). lub \(\Large =\frac{5}{2}\); glb\(\Large =\frac{3}{2}\)

B). lub \(\Large =\frac{-1}{5}\); glb\(\Large =\frac{3}{5}\)

C). lub \(\Large =\frac{1}{5}\); glb\(\Large =\frac{-1}{5}\)

D). none of these

-- View Answer

9). \(\Large \{ \frac{3n+2}{2n+1}n\in N \}\)

A). lub \(\Large =\frac{3}{5}\); glb\(\Large =\frac{3}{2}\)

B). lub \(\Large =\frac{5}{3}\); glb\(\Large =\frac{3}{2}\)

C). lub \(\Large =\frac{-1}{3}\); glb\(\Large =\frac{3}{2}\)

D). none of these

-- View Answer

10). \(\Large \{ x:x=1+\frac{1}{n};n\in N\}\)

A). lub = 1; glb = 0

B). lub = 2 ; glb = 1

C). lub = 3; glb = 0

D). none of these

-- View Answer