If you break 空 into its components, you find this:
穴 (KETSU, ana: hole) + エ (KŌ: construction)
According to Kenneth Henshall in A Guide to Remembering Japanese Characters, エ lends both sound and meaning to 空. Unfortunately, none of his explanations about this make anything snap into place for me. The best I can do for a mnemonic is to think of standing エ on its side, turning it into the English letter H. The H stands for “hole.” So in 空, 穴 (hole) + H (hole) means “empty.” That is, when 空 doesn’t mean “sky”!
I enjoy seeing how the top component (the “hole,” 穴) recurs in certain compounds:
穴空 hole + empty
Depending on which hiragana you add to this compound, you can produce the following phrases:
• ana (ga) a(ite iru): to be pierced with a hole
(You would write this out as 穴が空いている.)• ana (o) a(keru): to make a hole
(You would write this out as 穴を空ける.)
If you slice 穴空 in half and flip it around, you get 空穴:
空穴 (kara(k)ketsu: flat or stone broke) empty + hole
The meaning changes entirely with the inversion.