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Math Help - Defining the space mathematically in philosophical "fashion"

  1. #1
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    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 .

    Could anyone give ideas about this ?
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  2. #2
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    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.
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  3. #3
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    Re: Defining the space mathematically in philosophical "fashion"

    You mean mathematical models that physicists hypothesize about the space ?
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  4. #4
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    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).
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