gtk-window-stick (window)

window -- a gtk-window widget

Asks to stick the window, which means that it will appear on all user desktops. Note that you should not assume the window is definitely stuck afterward, because other entities, e.g. the user or window manager, could unstick it again, and some window managers do not support sticking windows. But normally the window will end up stuck. Just do not write code that crashes if not.

It is permitted to call this function before showing a window.

You can track stickiness via the "window-state-event" signal on the gtk-widget object.