Organodynamics	Grant Holland, Apr 25, 2014
Slide: Topological State – Formal Definition	Nav Refs Top Bottom Previous Next 90m 90m 45m 45m 25m 25m
MCD Model, continued Create a topology on S, our underlying (finite) set of atoms 1. Create CS, a cover of S. 2. Do this by using the molecules in S to create subsets of atoms. 3. Also create singleton subsets for “loose” atoms in S. Notice that some of the subsets in CS overlap – share some atoms (ions), because of covalent bonds. CS is, at this point, a (finite) cover of S. As a cover of S, it gives rise to a finite topology TS on S.	We are going to this finite topology TS as a way of organizing the atoms of S into “compartments” within the underlying set of atoms.
So, we have organized, by compartmentalization, our underlying set S of atoms, by defining a finite topology TS on S. Members (open sets) of TS represent all of the molecules currently in the MCD space, plus any “loose atoms”.	But, we also want to organize S by interrelationships as well as by compartmentalization. And we want our mathematical construct that represents the organization of S to include both representations. Next, we’ll try to enhance the topology on S that we devised in this slide so that it includes both views of organization.

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