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?
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 ...
Functional Analysis - 1) Let E be an infinite dimensional normed space, and let S =...
Find the weak closure of S.
Please see attached for full question.
Real Analysis : Density of Sets - Show that a set E is nowhere-dense in R if and only if the complement of E Closure (E on top bar) is dense in R.
Real analysis - Let A be bounded above so that s= sup A exists show that s belong to closure A(A over it bar)