Halliday & Matthiessen (1999: 69, 70):
We shall relate typology and topology to one another as complementary perspectives on meaning, and then we shall say a few words about the value of keeping the topological perspective in view. Let us start with our analogy from the expression plane: a vowel system can be construed both typologically as a set of systems, e.g. two systems 'front/ back' & 'open/ closed' defining four vowel values, and topologically as a two-dimensional space with four focal (core, cardinal vowel) locations. These two perspectives are related to one another in Figure 2-8.
Each system in the typology corresponds to a dimension in the topology. We can thus say that the two simultaneous systems correspond to a two-dimensional space. The systemic terms, or values, correspond to regions within the vowel space along one of its dimensions; an intersection of two systemic terms such as 'front* & 'open' is a region located along two dimensions. If we add further systems in the typology, e.g. rounding ('rounded/ unrounded'), nasality ('nasal/ non-nasal') and tongue root position ('neutral position/ advanced position'), these will correspond to further dimensions in the vowel space. With tongue root position we are still maintaining a reasonably congruent relationship between our representation of the vowel space and the oral cavity in which vowels are articulated, since advanced tongue root position is simply a global shift of the whole space; but with nasality we are beginning to use our representation more metaphorically, since the control of airflow through the nose is not a feature of the oral cavity.