Definition
An n-dimensional building X is an abstract simplicial complex which is a union of subcomplexes A called apartments such that
- every k-simplex of X is within at least three n-simplices if k < n;
- any (n – 1 )-simplex in an apartment A lies in exactly two adjacent n-simplices of A and the graph of adjacent n-simplices is connected;
- any two simplices in X lie in some common apartment A;
- if two simplices both lie in apartments A and A ', then there is a simplicial isomorphism of A onto A ' fixing the vertices of the two simplices.
An n-simplex in A is called a chamber (originally chambre, i.e. room in French).
The rank of the building is defined to be n + 1.
Read more about this topic: Building (mathematics)
Famous quotes containing the word definition:
“Although there is no universal agreement as to a definition of life, its biological manifestations are generally considered to be organization, metabolism, growth, irritability, adaptation, and reproduction.”
—The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on “life” (based on wording in the First Edition, 1935)
“... if, as women, we accept a philosophy of history that asserts that women are by definition assimilated into the male universal, that we can understand our past through a male lens—if we are unaware that women even have a history—we live our lives similarly unanchored, drifting in response to a veering wind of myth and bias.”
—Adrienne Rich (b. 1929)
“The very definition of the real becomes: that of which it is possible to give an equivalent reproduction.... The real is not only what can be reproduced, but that which is always already reproduced. The hyperreal.”
—Jean Baudrillard (b. 1929)