Answer:
a.No
b.No
c.No
Step-by-step explanation:
a.No,Such set does not exist .A set of natural numbers is N
Every point of this set is an isolated point but no accumulation point
Accumulation point:It is defined as that point a of set Swhich every neighborhood contains infinitely many distinct point of set
Isolated point : it is defined as that point a of set S which neighborhood does not contain any other point of set except itself
Interior point of set :Let .Then a is called interior point of set when its neighborhood is a subset of set S.
When a set is uncountable then interior point exist it is necessary for interior points existance .
Boundary points :Let .If every non empty neighborhood of a intersect S and complement of S.
Every member of a set is a boundary point
b.No, such set does not exist .A non empty set with isolated point then the set have no interior points .By definition of interior point and isolated point .For example.set of natural numbers
c.No, Such set does not exist ,for example set of natural every point is an isolated point and boundary point.By definition of boundary point and isolated point