Holey Space [espace troue]: the ‘third space’ of the machinic phylum (of matter-flow), inhabited by itinerant mettalurgists, and by extension the ‘underground’ space that can connect with smooth space and be conjugated by striated space. Holey space is the subsoil space of ‘swiss cheese’ that bypasses both the ground [sol] of nomadic smooth space and the land [terre] of sedentary striated space. In this bypassing, holey space is suspect; for Gilles Deleuze, the mark of Cain is not the biblical mark of the soild, but a mark of the subsoil [sous-sol], since holey space is conceived of by surface dwellers as created by theft and betrayal.
Holey space has different relations to nomadic smooth and State striated space. Cave-dwelling, earth-boring tunnellers are only imperfecty controlled by the State, and often have allied with nomads and with peasants in revolts against centralized authority. Thus the machinic phylum explored in holey space connects with smooth space to form rhizomes, while it is conjugated (blocked) by State striation.
The previously positive relation of holey and smooth space has turned around, however, now that States are able to create a smooth space of surveillance and global military interevention. Holey spaces have flourished for the only way to escape the spying eyes of State intelligence is to go underground: ‘Do not new smooth spaces, or holey spaces, arise as parries even in relation to the smooth space of a worldwide organization? Virilio invokes the beginnings of subterranean habitation in the “mineral layer”, which can take on very diverse values. Such a turnaround has not gone unnoticed; led by the Bush Administration, global States now trumpet the danger of ‘rogue regimes’ that have taken their weapons-making capabilities underground where they cannot be detected by satellites and spy planes. North Korea in 2003 remains the prime example, but much of the premise upon which the Bush Administration built its case for the 2003 ‘pre-emptive’ assault on Iraq was the supposedly concealed nature of weapons laboratories and storage facilities. The post 9/11 Afghanistan war was also launched against the holey space of the so-called ‘Al Qaeda’ network, supposedly in possession of innumerable underground hideouts, indeed even elaborate bunkers (though these were discovered to be not nearly as luxurious as their reputations). The bunkers and tunnels of the American establishment are, of course, exempt from any suspicion.
Cyberspace and forest space may also be seen as holey spaces rather than as smooth spaces in that they provide protective cover for ‘underground’ operations. Guerrilla armies such as the FARC (Fuerzas Armadas Revolucionarias de Colombia) use forests to great advantage, and indeed a long line of guerrilla forces in Latin American has used rain forests in this way. The armies of the State cannort array on it as on a battlefield, and the trees must be defoliated before air war can be successful. Cyberspace is filled with gaps and voids, black matter from which hackers (these may of course be in the service of States) launch coordinated attacks on sites and servers. A study of the paranoid tunneling in Cold War suburban backyards to create ‘fallout shelters’ would yield yet another aspect of the interrelations of smooth, striate, and holey space, as would the innumerable urban legends concerning sewers, subway tunnels, and the like.

Deleuze and geophilosophy: a guide and glossary by. Mark Bonta and John Protevi. Edinburgh: Edinburgh University Press, 2004