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QUIZ

University

Mathematics

49%

accuracy

9

plays

User image

4 years

Mathematics

University

Real analysis

user

9
plays

10 questions

10 questions

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1. Multiple Choice
30 seconds
1 pt
Let $\left(M_1,d_1\right)$ and $\left(M_2,d_2\right)$ be two metric spaces. A function f : $M_1\rightarrow M_2$ is continuous iff …......... in $M_1$ whenever F is closed in $M_2$
f(F) is closed
f^-1(F) is closed
f(F) is open
f^-1(F) is open
2. Multiple Choice
30 seconds
1 pt
If f is continuous bijection, $f^{-1}$ is also continuous
false
true
3. Multiple Choice
30 seconds
1 pt
R is connected.
true
false
4. Multiple Choice
30 seconds
1 pt
The function f:R $\rightarrow$ R defined by f(x)= sin x is uniformly continuous
true
false
5. Multiple Choice
30 seconds
1 pt
If f is continuous at ‘a’ iff lim x $\rightarrow$ a, f(x)=……………….
$\infty$
a
f(a)
0
6. Multiple Choice
30 seconds
1 pt
In any metric space union of any family of open set is ……. of each of its points.
open
closed
not open
not closed
7. Multiple Choice
30 seconds
1 pt
In the discrete metric space M the diameter of A={1,4,7,9} is ………..
8
1
9
0
8. Multiple Choice
30 seconds
1 pt
Which of the following is open in R?
Q
Z
Set of irrational number
(0,1)
9. Multiple Choice
30 seconds
1 pt
In R with usual metric [a,b) is
closed
open
both open and closed
neither open nor closed
10. Multiple Choice
30 seconds
1 pt
If M is discrete metric space then B(a,2)= ……………..
2
M
Φ
{a}
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