In this schematic they've somehow created "wireless" networks, meaning networks that connect two components but don't have an actual wire in the schematics.
What are these called, and how can I create them in Eagle Cad 6.5?
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These are simply named nets, which will automatically be connected together.
They are used for off-sheet connections (in designs with multiple schematic sheets) and also to reduce the mess of wiring in complicated designs. Many people seem to dislike them if they are overused on a schematic though, it can make it quite hard to follow.
In EAGLE there are two steps, naming and labelling.
Firstly use the NAME tool, click the net (wire) and give it a sensible name. Note that if you name two wires like this they will become connected, you do not need to do anything further.
Don't forget that you can type NAME and hit enter to get into this tool.
Next use the LABEL tool to add a graphical indicator that the net is named. Remember that you don't need to do this, but it does make the schematic clearer.
On the top menu you can change the style, by default it is a simple text label. The second button (pressed in the screenshot) will set the style to the 'arrow'.
You can give a net a name. Nets with the same name are connected, even when there is not visible line between them. For clarity, add a label to every occurrence. I know no way to make those nice 'arrow labels' in Eagle. To save myself some typing effort, I often create a bus with the common net names. By terminating a net on the bus, you can choose the name from a dropdown list. Later I add the labels and move or even delete the bus.