In an integration network, an outer space relation is a vital relation that holds between counterparts across input spaces. This contrasts with the notion of an inner-space relation.

To illustrate, consider the boat race blend, discussed by Gilles Fauconnier and Mark Turner, and prompted for by the following utterance: As we went to press, Rich Wilson and Bill Biewenga were barely maintaining a 4.5 day lead over the ghost of the clipper Northern Light. This example relates to a 1993 news story in which a modern catamaran Great American II, sailed by Wilson and Biewenga, set out on a route from San Francisco to Boston. A record for this route had been set in 1853 by the clipper Northern Light, which had made the journey in 76 days and 8 hours.

This record still held in 1993. The utterance above prompts for an integration network in which there are two input spaces: one relating to the journey of the modern catamaran in 1993 and the other relating to the original journey undertaken by the Northern Light in 1853. The generic space contains schematic information relating to boats and journeys, which motivates matching and thus cross-space connectors between counterparts in the two input spaces. In the blended space, we have two boats: Great American II and Northern Light. Moreover, in the blend the two boats are engaged in a race by virtue of schema induction which recruits a race frame. In this boat race blend, the modern catamaran is conceptualized as barely maintaining a lead over the Northern Light.

The outer-space vital relations are designated by the lines relating counterparts in the input spaces. The vital relation that connects the catamaran/clipper and Wilson and Biewenga/crew is that of identity. The outer-space vital relation connecting the two dates 1853 and 1993 is that of time. The outer-space relation connecting the specific locations on the course of the two boats at any given point during their respective journeys is that of space.