The Nikkei stock index closed at an all-time high Tuesday for the third consecutive trading day, eking out gains amid persistent optimism for the U.S. economy and Japanese stocks. The 225-issue Nikkei Stock Average ended up 5.81 points, or 0.01 percent, from Monday at 39,239.52. The broader Topix index finished 4.84 points, or 0.18 percent, higher at 2,678.46, its highest level since February 1990. On the top-tier Prime Market, gainers were led by iron and steel, bank and machinery shares. The U.S. dollar fell slightly to the mid-150 yen range after Japan’s core inflation slowed to 2.0 percent…