Examples
For example, let be a vector space over a field, and, for, define to be the span of, that is, the set of linear combinations of elements of . Then the pair is a pregeometry, as it is easy to see.
In contrast, if is a topological space and we define to be the topological-closure function, then the pair will not necessarily be a pregeometry, as the finite character condition (4) may fail.
Read more about this topic: Pregeometry (model Theory)
Famous quotes containing the word examples:
“Histories are more full of examples of the fidelity of dogs than of friends.”
—Alexander Pope (1688–1744)
“It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
—G.C. (Georg Christoph)
“No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
—André Breton (1896–1966)