Recent content by shapiro478

Say a function f and its derivative are everywhere continuous and of exponential order at infinity. F(s) is the Laplace transform of f(x). I need to find the limit of F as s goes to infinity. I use the integral definition of the Laplace transform and the fact that f is of exponential order...

Say f is a continuous function on R. How could I find two linearly independent solutions of (y' + f(x)y)' = 0? Notice that there is no hypothesis about f being differentiable, so the obvious method of attack (taking the derivative of each term in the parenthesis and working off the resultant...

Office_Shredder -- I don't believe the epsilon-ball notion of open is valid here since we're working in some arbitrary topology "X", which is not necessarily the normal topology.

rs1n -- This new approach looks a lot more promising. I just have a question or two about this approach. M is a bunch (or even infinite number) of open subsets of X. When you intersect M with F, how do you know that the resultant intersection is still comprised of sets open in F? (is this an...

so it looks good JasonRox? thanks for your help

JasonRox -- The hypothesis does say C is compact in F... "If C is contained in F and compact in F..." Compact means every open cover has a finite subcover

Say X is a topological space and F is in X. If C is contained in F and compact in F, then C is compact in X. This is obvious when you draw a picture, but proving it is a little more difficult. By hypothesis, C is compact in F so C has a finite subcover M, with M being the union of m_1, m_2...