Define the Punctured neighbourhood of a. - Vidyadip

Question

Define the Punctured $\delta$ neighbourhood of $a.$

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Answer

If $a \in R$ and $δ$ is non-negative real number then the open interval $(a -δ ; a + δ) - \{a\}$ is called punctured δ neighbourhood of $(A)$ It is denoted by $N*(a, δ).$
$N*(a, δ) = N*(a, δ) - \{a\}$

$= \{x/a -δ < x < a + δ; x \neq a; x \in R\}$
$= \{x/|x-a| < δ; x \neq a; x \in R\}$

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