![]() ![]() ![]() The concept was first introduced by John von Neumann and Andrey Kolmogorov in 1935. The key to this realization lay in Einstein's demonstration that, since matter warps space, the sum total of the mass in all the galaxies might be. ![]() The universe to be finite means in this context basically that it is bounded (by some maximal expansion or radius). If the universe is more or less it would be unbounded. In functional analysis and related areas of mathematics, a set in a topological vector space is called bounded or von Neumann bounded, if every neighborhood of the zero vector can be inflated to include the set.Ī set that is not bounded is called unbounded.īounded sets are a natural way to define locally convex polar topologies on the vector spaces in a dual pair, as the polar set of a bounded set is an absolutely convex and absorbing set. General relativity resolved the matter by establishing that the universe could be both finite i.e., could contain a finite number of stars in a finite volume of space and unbounded. A finite subset S of the reals is totally ordered and therefore (being finite) has a first and last element f and l with the property that f x l f x l for all x in S. A bounded (metric space) means any two points cant be further away than a certain number, a maximal distance or radius. It seems the observable universe is limited by our event horizon at some 14 billion light years. It was the whole universe that went bang and started expanding. The moot point is that the Big Bang didn't go bang within the universe. For bounded sets in general, see bounded set. When you wind the timeline back, you get to the point where the whole universe was 'the size of a grapefruit'. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |