Set theory
Blue signifies Kingdom
The closed-set model:
A 'closed set' is defined by a boundary - all that is inside belongs to the set, all that is outside does not.
Applying this to the Church, 'closed set' believers have a 'territorial' concept of God's kingdom, enclosed within a boundary. Membership comes through crossing the boundary in an act of conversion. Once inside Kingdom territory, care must be taken not to cross the boundary again.
An 'open set' has no 'territorial' boundary, but is defined by relationship with a centre: all that is moving towards the centre, seeking relationship, belongs; all that is moving away, abandoning relationship, does not.
For 'open set' believers, membership of the Kingdom is defined by movement towards or away from Christ as centre. There are still those that belong and those that don't, but you can't separate them easily by drawing a boundary, let alone state who's in and who's out once and for all. Those who appear to be close to Christ may be moving away from him, those that seem far away may be heading towards him.
Network or liquid church as a function of the open-set model:
In the open-set model the Church appears as a fluid network of relationships. The shape and structure of the Church changes constantly as components move and connections change. It cannot be frozen at one moment in time, or fixed in a particular pattern. Any maps of the Church are snapshots and provisional readings.
