0

Does a space require more than one dimension? For instance $\Bbb R$ is not a space but $\Bbb R^2$ is?

Andrés E. Caicedo
  • 79,201
Charlie
  • 685
  • 3
    A space is typically a set with more properties, and so will have an adjective such as "vector space", "topological space", or "Hilbert space" along with it. – Dayton Nov 29 '19 at 22:23

1 Answers1

3

A space often, but not exclusively, refers to a topological space; that is, a set with a distinguished collection of open subsets. Under this lens, $\mathbb{R}$ is a space in many ways, but at least in the Euclidean topology.

Dimension is not a restriction to being a space.

Eric
  • 1,632
  • 1
    So there is no such thing as just a "space", it must fall into one of the different types of spaces e.g. Vector, Hilbert, Topolgoical? – Charlie Nov 29 '19 at 22:33
  • 1
    @Charlie, that’s right. Calling something a “space,” it should be clear from the context what that word should mean. – Eric Nov 29 '19 at 22:36