Building (mathematics)

In mathematics, a building (also Tits building, Bruhat–Tits building, named after François Bruhat and Jacques Tits) is a combinatorial and geometric structure which simultaneously generalizes certain aspects of flag manifolds, finite projective planes, and Riemannian symmetric spaces. Initially introduced by Jacques Tits as a means to understand the structure of exceptional groups of Lie type, the theory has also been used to study the geometry and topology of homogeneous spaces of p-adic Lie groups and their discrete subgroups of symmetries, in the same way that trees have been used to study free groups.

Overview

The notion of a building was invented by Jacques Tits as a means of describing simple algebraic groups over an arbitrary field. Tits demonstrated how to every such group G one can associate a simplicial complex Δ = Δ(G) with an action of G, called the spherical building of G. The group G imposes very strong combinatorial regularity conditions on the complexes Δ that can arise in this fashion. By treating these conditions as axioms for a class of simplicial complexes, Tits arrived at his first definition of a building. A part of the data defining a building Δ is a Coxeter group W, which determines a highly symmetrical simplicial complex Σ = Σ(W,S), called the Coxeter complex. A building Δ is glued together from multiple copies of Σ, called its apartments, in a certain regular fashion. When W is a finite Coxeter group, the Coxeter complex is a topological sphere, and the corresponding buildings are said to be of spherical type. When W is an affine Weyl group, the Coxeter complex is a subdivision of the affine plane and one speaks of affine, or Euclidean, buildings. An affine building of type is the same as an infinite tree without terminal vertices.

Building (disambiguation)

A building is a constructed object intended for occupancy by humans or animals.

Building may also refer to:

See also

Online creation

Online creation, also referred to as OLC, online coding, online building, and online editing, is a software feature of MUDs that allows users to edit a virtual world from within the game itself. In the absence of online creation, content is created in a text editor or level editor, and the program generally requires a restart in order to implement the changes.

Online creation as original content

An aspect of online creation that separates it from "mere game play" is that online creation systems can generally be used to create new content — new objects, new locations, new creatures — rather than simply creating instances of predefined items in the game world. Some have observed that certain forms of online creation — notably those associated with creating new commands — can threaten the stability of the server.

History

Origins

The first publicly available MUD that featured in-game creation of the game world was Skrenta's 1988 Monster.

Town

A town is a human settlement larger than a village but smaller than a city. The size definition for what constitutes a "town" varies considerably in different parts of the world.

Origin and use

The word town shares an origin with the German word Stadt, the Dutch word tuin, and the Old Norse tun. The German word Zaun comes closest to the original meaning of the word: a fence of any material. An early borrowing from Celtic *dunom (cf. Old Irish dun, Welsh din "fortress, fortified place, camp," dinas "city;"

In English and Dutch, the meaning of the word took on the sense of the space which these fences enclosed. In England, a town was a small community that could not afford or was not allowed to build walls or other larger fortifications, and built a palisade or stockade instead. In the Netherlands, this space was a garden, more specifically those of the wealthy, which had a high fence or a wall around them (like the garden of palace Het Loo in Apeldoorn, which was the example for the privy garden of William and Mary at Hampton Court). In Old Norse tun means a (grassy) place between farmhouses, and is still used in a similar meaning in modern Norwegian.

Man About Town

Man About Town may refer to:

Town (Vietnam)

In Vietnam, there are two kinds of diministrative subdivisions that can be translate into town or township: