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Sophie [7]
3 years ago
9

Prove the isolated and the interior points of a set must belong to the set, but give examples to show the limit points and bound

ary points of a set may or may not belong to the set.
Mathematics
1 answer:
Irina-Kira [14]3 years ago
6 0
By definition, an isolated point x of a set S is a point of S. 
Also, an interior point of a set S can be defined by the mean of the 
existence of a positive number r>0 such that :
D(x,r)\subset S\text{ therefore }x\in S
wherein D(x,r) is the disc of center x and radius r. 

Example of a set whose boundary is not a subset of S:

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