Organodynamics	Grant Holland, Apr 25, 2014
Slide: Extended Topological State	Nav Refs Top Bottom Previous Next 90m 90m 45m 45m 25m 25m
MCD Model, continued We shall now extend our topology on S, to include a representation of the interrelationships among the atoms of S. Here’s how: 1. For each open set in TS, create a set of ordered pairs (relation) that describes how the atoms in that open set are chemically bonded. 2. For each open set in TS, pair the open set with the relation. This creates the pair (ri, si), where ri is the open set and si is the relation. 3. Collect all of these pairs (ri, si), one for each open set in TS, into a set named OTRS.	OTRS is called an organization on S. We also refer OTRS as an “extended topology” on S. This definition provides a topologically-based construct, OTRS, that organizes S with respect to both compartmentalization and interrelationships. Organodynamics uses subspace topologies to represent nested organization. For example, molecules within molecules… (See Part II, “Implementing Composite State”)
An extended topology, OTRS, represents how a set S can be organized. As such, an OTRS instance defines state in organodynamics.	Thus, the set of all possible OTRS on S is a state space in organodynamics. We name the state space OS. Thus, OS is the state space in organodynamics.

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