🔶06 - 𝛿 Neighbourhood of a Point and Deleted 𝛿 Neighbourhood of a Point | Open and Closed Set

🔶06 - 𝛿 Neighbourhood of a Point and Deleted 𝛿 Neighbourhood of a Point | Open and Closed Set
In this video, we shall study the neighbourhood of a point and the deleted neighbourhood of a point.
The neighbourhood of a point is the open interval containing that point where one can move some distance away from that point without leaving the interval.
The 𝛿 neighbourhood of a is given by the open interval (a-𝛿, a+𝛿), for such interval
1. a-𝛿 and a+𝛿 are not part of the set, but a is part of the set
2. the interval is centered at a
3. the length is given by 2𝛿

The 𝛿 deleted neighbourhood of a is given by the open interval (a-𝛿, a) U (a, a-𝛿). For such an interval
1. a-𝛿 and a+𝛿 as well as a is not part of the set
2. the interval is centered at a
3. the length is given by 2𝛿

Open Set is a set which does not contain any of its boundary point eg (1,2)

Closed Set is a set which contains all its boundary point eg [2, infinity)
00:00 - 𝛿 neighbourhood of a
05:22 - Example of 𝛿 neighbourhood of a
10:07 - deleted 𝛿 neighbourhood of a
14:07 - Example of deleted 𝛿 neighbourhood of a
17:51 - Open Set
20:10 - Closed Set

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