What connection was made between imperialism and the american frontier?

The connection was that in the 1890 census the frontier was closed, meaning that the U.S. had no open west that we identify in the 21st century with cowboys and sleepy mine towns.  This announcement had a great effect on the American psyche as there had always been western land to expand into but now that the frontier was gone there was no more western land to go to.  The United States always saw itself as a nation that constantly expanded and as a result looked overseas.  American imperialism was a natural continuation of the old tendency of westward expansion that wished to see the U.S. grow and the U.S. needed more land to exploit economically such as Hawaii.

Ship building industry , good luck : )