Neighbourhood, Interior point and Openset

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In this video will learn what is meant by the neighborhood of a point, interior point, and open set.
Note: What is meant by metric space?
Let X be a set. A metric on X is a mapping d: X x X -- R. Statisfing the following properties.
d(a,b) greater than 0, if a b. d(a,b) = 0, if a = b;
d(a,b) = d(b,a);
d(a,c) less than or equal d(a,b)+d(b,c);
Where a, b and c belongs to X.
The neighborhood of a point p of radius r N(p,r):
Set of all points q such that d(p,q) less than r.
Example1) On real line N(p,r)= {q : |p-q| less than r }
Example 2) One R2 N(p,r) = {q : || p-q || less than r}
Interior points:
A point p is called interior point of a set S, if N(p,r) contained in S.
Open set:
If all points of S are interior points then the set S is an open set.