Woolworths Limited is the largest retail company in Australia and New Zealand. Although named after the F.W. Woolworth Company (as developed in USA), it has no other connection with its U.S. namesake
That said, "Woolworths opened its first store, the Woolworths Stupendous Bargain Basement, in the old Imperial Arcade in Pitt Street, Sydney, on 5 December 1924."