Quotient Space Based Problem Solving

1.5. Property-Preserving Ability

1.5.1. Falsity-Preserving Principle

We have discussed the relation between the domains [X] and X. For a problem space (X, f, T,), structure T is very important. When a domain X is decomposed, its structure will change as well. Generally, it is simplified. The main point is whether some properties (or attributes) in X that we are interested in are still preserved after the simplification.

Generally speaking, there is a wide variety of structures. It is difficult to make a general discussion. We'll focus our attention on two common cases, i.e., topologic structure and semi-order structure. Although semi-order is one of topologic structures, due to its particularity we still discuss them separately.

1.5.1.1. Structure ...