Prove:
If H is a closed point set and p is a point of S - H, then there exist open point sets U and V containing H and p respectively such that cl(U) and cl(V) are disjoint.
Closure - Prove:
If H and K are disjoint closed point sets, then there exist open point sets U and V containing H and K respectively such that cl(U) and cl(V) are disjoint.
Closure - Prove:
If p and q are points, then there exist open point sets U and V containing p and q respectively such that cl(U) and cl(V) are disjoint.
Real Analysis : Elementary Sets and Closure - 1). Let M be an elementary set. Prove that | closure(M)M | = 0. ( closure of M can also be written as M bar, and it is the union of M and limit points of M).
2). If M and N are elementary sets then ...
More trouble with n-space - How do I prove the following:
Sbar - S with an over score
Let S' denote the derived set and Sbar the closure of a set S in Rn. Prove that
(Sbar)' = S' and Sbar is closed in Rn
Real Analysis : Connected and Disconnected Sets and Closure - a- Find an example of a disconnected set whose closure is connected.
b- If A is connected ,is A closure necessarily connected? If A is perfect is A closure necessarily perfect?