What is the definition of 'space'?

In summary, "space" is a general and important mathematical construct with various types such as vector spaces, metric spaces, and topological spaces. A space is defined as a set with additional structure and properties, and there may be a rigorous definition in the field of category theory.
  • #1
quasar987
Science Advisor
Homework Helper
Gold Member
4,807
32
Mathworld's definition: "The concept of a space is an extremely general and important mathematical construct. Members of the space obey certain addition properties."

It is quite vague. What would a rigourous definition be?
 
Mathematics news on Phys.org
  • #2
Notice that it says "a space" not just "space". There are a number of different kinds of "spaces" used in mathematics (vector space, topological space (in which members do not "obey certain addition properties"!), etc.).

If you want a definition of "space" (that in which we all live), then you should ask in a physics forum.
 
  • #3
In the most abstract sense,u can't have a space without a set.So the notion of "set" is the trully elementary one.A space is a set whose elements & subsets have certain properties.U can't be too rigurous,really.

Daniel.
 
  • #4
There isn't really a rigourous defintion, but ea space si basically a ste with some additonal structure defined on it.

So for exmaple a vector space has the addiotnal structure of an asosciated field, vector additon and scalar mulpilcation; a metric space has the additonal structure of a metric function; a topological space as the additonal structure of a topology and so on.
 
  • #5
I bet there's got to be a category theorist out who can take these general notions and come up with a general rigorous definition. Like a space is a collection of sets, an operation between the sets and a set of axioms that must be satisfied. ie one of the sets in the collection would be the elements of the space, another set could be a topology on the space and the operation between those two sets would be inclusion.

I'm not saying this would be the categorist's definition but I bet there is one. A categorist just can't help but to generalize these sorts of things.
 

Related to What is the definition of 'space'?

What is the definition of 'space'?

Space is the vast, three-dimensional expanse that surrounds us and contains all matter and energy in the universe.

How do scientists define 'space'?

Scientists define space as the three-dimensional volume in which objects exist and move, and is characterized by its dimensions of length, width, and height.

What is outer space?

Outer space, also known as just "space", refers to the region beyond Earth's atmosphere and between celestial bodies, where there is a near-vacuum and very low density of matter.

Is there a boundary to space?

There is no universally agreed upon boundary to space, as it is constantly expanding and changing. However, the most commonly accepted boundary is the edge of Earth's atmosphere, known as the Karman Line, which is approximately 62 miles above the Earth's surface.

How is space studied and explored?

Space is studied and explored through various scientific disciplines, such as astronomy, astrophysics, and cosmology. Scientists use telescopes, satellites, probes, and manned missions to gather data and explore the mysteries of space.

Similar threads

Replies
10
Views
795
  • General Math
2
Replies
61
Views
9K
Replies
4
Views
1K
Replies
18
Views
1K
  • Linear and Abstract Algebra
Replies
8
Views
1K
  • Special and General Relativity
2
Replies
37
Views
2K
Replies
21
Views
2K
  • Differential Geometry
Replies
21
Views
801
  • General Math
Replies
7
Views
4K
  • General Math
Replies
22
Views
1K
Back
Top