Real analysis

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

 If f is continuous bijection, $f^{-1}$   is also continuous

• false

• true

Tags

CCSS.HSF.BF.B.4

R is connected.

• true

• false

Tags

CCSS.HSA.REI.D.11

The function f:R  $\rightarrow$  R defined by f(x)= sin x is uniformly continuous

• true

• false

If f is continuous at ‘a’ iff lim x $\rightarrow$  a, f(x)=……………….

•  $\infty$  

• a

• f(a)

• 0

In any metric space union of any family of open set is ……. of each of its points.

• open

• closed

• not open

• not closed

In the discrete metric space M the diameter of A={1,4,7,9} is ………..

• 8

• 1

• 9

• 0

Which of the following is open in R?

• Q

• Z

• Set of irrational number

• (0,1)

In R with usual metric [a,b) is

• closed

• open

• both open and closed

• neither open nor closed

If M is discrete metric space then B(a,2)= ……………..

• 2

• M

• Φ

• {a}