Complete metric space, open and dense

Let X be a complete metric space....(see attached)

Factoring Polynomials

I need some help with these problems. Please see attachment. Please show all work to each equation Factor out the GCF in each expression 1) 15x^2y^2 - 9xy^2 + 6x^2y 2) a(a + 1) -3(a + 1) Factor each polynomial completely 3) x^3y + 2x^2y^2 + xy^3 Use grouping to factor each polynomial completely 4) x^3 ...continues

Real Analysis Proof

Prove that a set S included R has no cluster points if and only if S intersection [-n,n] is a finite set for each n in N.

Closure in Real Analysis

Let A be a subset of R^n. Show that the characteristic function Xa is continuous on the interior of A and on the interior of its complement A' but is discontinuous on the boundary ∂A = A (bar)∩A' (bar)

Derive from logarithm and exponent laws

x^y=e^(ylogx)

Prove where p>1 is a real number

Prove where p>1 is a real number-->1/((1-p)^-s)=1+1/(p^s)+1/(p^2s)+1/(p^3s)+1/(p^4s)+1/(p^5s)+.. Which values of s is it valid?

Interior points of a set

Show that a set A is open iff A = the set if interior points of A

Set of interior points

Prove that the set of interior points of a set A is equal to the union of open sets O, such the O is a subset of A

Real Analysis problem

See the attached file Justify Euler's equality....

Closed set

A set F is closed iff for all x_n in F for all n in the naturals (x_n) converges to l, then l is in F. (x_n) is a sequence