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Metric Spaces

Authored by Indulal Gopal

Mathematics

University

Used 295+ times

Metric Spaces
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30 questions

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1.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Let d be a metric on X. Then the symmetry property of d is

d(x,y)0d\left(x,y\right)\ge0

d(x,y)=d(y,x)d\left(x,y\right)=d\left(y,x\right)

d(x,y)=0 d\left(x,y\right)=0\ if and only if x=yx=y

2.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

The usual metric d on R is given by

d(x,y)=x+yd\left(x,y\right)=x+y

d(x,y)=xyd\left(x,y\right)=\left|x-y\right|

d(x,y)=x+yd\left(x,y\right)=\left|x+y\right|

3.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Te metric defined by   d(x,y)=0 if x=y and 1 if xyd\left(x,y\right)=0\ if\ x=y\ and\ 1\ if\ x\ne y  is 

indiscrete 

discrete

serpinski

usual

4.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

The distance function in usual sense is

a metric

not a metric

5.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

In Real analysis R is equipped with which metric

discrete

indiscrete

usual

cannot say unless the topology is mentioned

6.

MULTIPLE SELECT QUESTION

5 mins • 1 pt

Media Image

Which metric is discussed in the this figure? ( may be more than one answer is correct)

usual metric on R

discrete metric on R

distance metric

Indiscrete metric on R

7.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

The triangle inequality of a metric d says

d(x,y)=d(y,z)d\left(x,y\right)=d\left(y,z\right)

d(x,y)=d(x,z)+d(y,z)d\left(x,y\right)=d\left(x,z\right)+d\left(y,z\right)

d(x,y)d(x,z)+d(z,y)d\left(x,y\right)\ge d\left(x,z\right)+d\left(z,y\right)

d(x,y)d(x,z)+d(z,y)d\left(x,y\right)\le d\left(x,z\right)+d\left(z,y\right)

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