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 .
Could anyone give ideas about this ?
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 .
Could anyone give ideas about this ?
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.
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).