Not using the language of this article. Referring to e.g. a two-dimensional space as "Dimension 2" is irregular. One might say that the space has dimension 2 (as shorthand for "has a dimension of 2"), but "Dimension 2" is not used as the proper name of such a space.
It's common in math to say things like "in dimension 2" to mean "when the dimension is 2". It doesn't necessarily refer to a specific space (although it could based on context). It's just setting a contextual variable. Many problems occur in varying dimension and oftentimes you want to restrict discussion to a specific dimension.
Right - what I meant specifically is the use of names like "Dimension 2" (with the capital D) as if to refer to a specific location with that name. Among other things, it has too many associations with pulp science fiction. :)
