The dollar's getting stronger and it's further weakening European banks to the point where some could soon shut their doors.   Just since June, there have been five increases in the swap from euros to dollars.  It's now estimated, according to Financial Times, the dollar gap has climbed to a half trillion dollars.  It's the old story of the world running to the safety of the US dollar when their own currency is threatened.  As weak as the dollars is, comparitively it's seen as a safer place to be with the possibility of an imminent Greek deflault.  Greece's repeated assurance that it will hold off default at all costs, isn't having much positive effect on worried investors.  Economist Don Smith at Icap says, "More and more euro banks want dollars, because of worries  about the debt crisis in Europe.  This leads to a vicious circle where the cost to swap dollars for euros rises and creates even more strains and potentially deeper problems for the financial sector."   Dollar gap funding took Lehman Brothers down in New York 3 years ago with double the present euro gap.  Money strategists fear a significant run on dollar-euro could overcome the euro banking system in the coming days or weeks.