Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4666202 | Advances in Mathematics | 2013 | 52 Pages |
Abstract
The counterparts of the Urysohn universal space in the category of metric spaces and the GurariÇ space in the category of Banach spaces are constructed for separable valued Abelian groups of fixed (finite) exponents (and for valued groups of similar type) and their uniqueness is established. Geometry of these groups, denoted by Gr(N), is investigated and it is shown that each of Gr(N)'s is homeomorphic to the Hilbert space â2. Those of Gr(N)'s which are Urysohn as metric spaces are recognized. 'Linear-like' structures on Gr(N) are studied and it is proved that every separable metrizable topological vector space may be enlarged to Gr(0) with a 'linear-like' structure which extends the linear structure of the given space.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Piotr Niemiec,