(np) wolfram & wikipedia on space

[Michael Bailey]

http://mathworld.wolfram.com/Space.html

The concept of a space is an extremely general and important
mathematical construct. Members of the space obey certain addition
properties. Spaces which have been investigated and found to be of
interest are usually named after one or more of their investigators.
This practice unfortunately leads to names which give very little
insight into the relevant properties of a given space.

The everyday type of space familiar to most people is called Euclidean
space. In Einstein's theory of Special Relativity, Euclidean
three-space plus time (the "fourth dimension") are unified into the
so-called Minkowski space. One of the most general type of
mathematical spaces is the topological space.

------------- certain addition properties?  at first I thought they
meant "additional" but I think they mean that the operation of
addition works in a specified way inside a *space* as versus inside a
*set*



wikipedia is really concise, although the article goes on (and on)
from the definition:

http://en.wikipedia.org/wiki/Space_(mathematics)

"In mathematics, a space is a set with some added structure."