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Let M be any non-empty set Define \[d(x,y)=\begin{cases}0\text{ if }x=y\\1\text{ if }x\ne y\end{cases}\] This metric is called

A) Stanaard Metric
B) Discrete Metric
C) Absolute Metric
D) Bounded Metric

Correct Answer:


B) Discrete Metric

Description for Correct answer:
Let M be a set for \(x,y\in M\)

The metric \[d(x,y)=\begin{cases}0\text{ if }x=y\\1\text{ if }x\ne y\end{cases}\]

is called discrete metric on M.

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

Comments

Similar Questions

1). Which of the following is not correct?

A). In a discrete metric space every-subset is open

B). \(\phi\) is open 3

C). Union of any family of open set is open

D). Arbitrary intersection of ope'nI sets is open

2). Let R be a metric space with usual metric \(\Large A_{n}= \left(\frac{-1}{n},\frac{1}{n}\right) \). Then \(\Large\bigcap\limits_{n=1}^{\infty}A_{n}\) is

A). open

B). not open

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D). half-open

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B). mutually disjoint closed sets

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5). Every convergent sequence is a

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B). optimal sequence

C). increasing sequence

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10). If a surface is developable then its Gaussian curvature is

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