The topological ontology defines a relation to express the fact that
mereological individuals are connected. We want to use this relation to
define connections in the component view of a physical system, where
being connected means *being able to exchange energy*. Because we
have this application in mind, the topology must be capable of stating
three things:

- Express that two individuals are connected.
- Multiple connections between components must be possible.
- It must be possible to say that a connection is of a certain type.

A well known way of expressing topological information is described by
B. L. Clarke [Clarke, 1981]. He introduces a relation *Cx*,*y* to
express that individuals *x* and *y* are connected. Unfortunately,
given this relation, it is only possible to express that there are two
connections between two individuals when connections are regarded as a
special kind of individuals themselves. We find this point of view
debatable, because a physical connection can be a point of contact
(mechanical, electrical), an area crossing a volume flow (hydraulical,
pneumatical) or even something abstract as a field (electro-magnetic).
We have therefore introduced connections as a relation between
individuals and reified the relation into the connection concept to
allow for multiple connections that can be typed. This has led to the
relation `connects(c,x,y)` which means that individuals `x` and
`y` are connected by connection `c` (see Figure 4).

**Figure 4:**
Excerpt from the topological ontology. This ontology provides the
means to express that individuals are connected. Axioms ensure that
only sound connections can be made. These axioms take into account
the possible part-of decomposition an individual can have.

The projection performed in this ontology is of the type *include
and extend*. Inclusion is done in line 2 and the extension takes shape
by definition of new concepts and relations that use mereology in their
axioms. This yields an ontology that has the same level of abstraction
as the included mereology. There are three axioms concerning
connections. The symmetry of the connection relation is expressed by
axiom 4a. Axiom 4b prohibits that a part is connected to itself or
its whole (`part-of(x,y)` holds iff `x` is a proper part of
`y` or they are equal). The third axiom (4c) ensures that when a
part whose whole is disjoint with an individual connected to the part,
the whole is also connected to that individual. The fourth axiom (4d)
prohibits a connection to connect two entirely separated pair of
individuals. This also excludes connections that fork.

Fri Sep 27 13:28:43 MET DST 1996