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A set T (a subset of R) is called neighbourhood of a point s if for any positive number e>0,the open interval (p-e,p+e) is a subset of T

It is also given that any open interval is neighbourhood of all its points.

let us take an example

(2,3) is an open interval and according to the definitions given above it is neighbourhood of all its points

so it will be a neighbourhood of any of its points,say, 2.1 if we take any positive number,say .1

then 2.1 belongs to (2,2.2) which inturn is a subset of (2,3)

what if we take our positive number to be .2

in this case 2.1 belongs to (1.8,2.4)which isn't a subset of (2,3)

is there a restriction that we need to choose a very small positive number?

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# Neighbourhood of a point

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