# Defining the space mathematically in philosophical "fashion"

• Jun 5th 2012, 03:44 AM
Mhmh96
Defining the space mathematically in philosophical "fashion"
Hello,,

I am looking for something like definition for the space ,not so much rigorous but a definition that utilize the mathematical concepts with some philosophy .

• Jun 5th 2012, 07:54 AM
HallsofIvy
Re: Defining the space mathematically in philosophical "fashion"
What do you mean by "the space"? I know a number of different types of "spaces" used in mathematics but I suspect you are talking about "physical space". In that case, I would first caution you that mathematics is not physics and how you represent anything physical in terms of mathematics depends upon the particular model you choose.
• Jun 6th 2012, 01:32 AM
Mhmh96
Re: Defining the space mathematically in philosophical "fashion"
You mean mathematical models that physicists hypothesize about the space ?
• Jun 8th 2012, 08:09 AM
Deveno
Re: Defining the space mathematically in philosophical "fashion"
it's hard to know if you are asking the question: "what is space-ness?" or, "what kind of mathematical structure best models the common ordinary intuition of space?".

several different kinds of things are called "spaces" in mathematics, it is a very general term. most of these are sets with various kinds of structure on them.

probably the closest to what we ordinarily regard as "physical space" is the notion of a topological vector space, a setting in which we can perform geometry and analysis. idealized objects such as "balls, spheres, tubes, etc." can often be realized as manifolds embedded within a topological vector space, which has proven very useful (especially in physics).

"which" manifold our universe might actually be, is not an entirely agreed-upon matter. the leading candidate these days is a 4-dimensional space-time continuum with an minkowski metric tensor, but this might be replaced with a more sophisticated model in the future (just as euclidean geometry was gradually replaced by more flexible notions of geometry).