I am downloading macOS High Sierra. System is asking me to close other applications, but there aren't any open.
I am being prompted to close other applications, but I do not have any open.
iMac, OS X Yosemite (10.10.5)
There are some things open, clearly, but not to worry. The installer should be able to close all of them. However, this shouldn't be needed in order to download the High Sierra installer. Perhaps there is more to this than you have disclosed?