Can an element be both boundary as well as limit point in a
Posted: Mon Feb 11, 2008 5:32 am
Is it possible for an element in a topology to be both boundary as well as limit point for a set?
e.g. S = {1,2,3}
Let us say 0 is null set then
T = {0, {1,2},{3},S} defines a toplogy on it.
Let is say A={1,3}
Can I have a case where a particular element of A is both limit point as well as boundary point of A.
TAKE THE CASE GIVEN ABOVE AS AN EXAMPLE ONLY.
e.g. S = {1,2,3}
Let us say 0 is null set then
T = {0, {1,2},{3},S} defines a toplogy on it.
Let is say A={1,3}
Can I have a case where a particular element of A is both limit point as well as boundary point of A.
TAKE THE CASE GIVEN ABOVE AS AN EXAMPLE ONLY.